Five years after he graduated with an economics degree from Princeton, Thomas Gilbert Jr walked into a Hamptons surf shop and asked if they needed an instructor.

At 29, Gilbert — who grew up in Manhattan’s elite social circles with wealth and connections — might have been expected to climb to the top of the world of finance, as his father and uncle had done.

Instead, the son of a successful hedge fund founder was surfing, going to exclusive social clubs and living on a $1,000 (£795) weekly allowance from his parents.

After three weeks of testimony in Gilbert’s murder trial, a picture of him has emerged as a perpetual Peter Pan who was increasingly troubled with the idea of losing his real life Neverland.

Gilbert’s lawyer maintains that mental illness problems are to blame for his client’s seeming inability to hold a steady job.

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But prosecution witnesses have described Gilbert as a feckless young man interested mostly in pleasurable pursuits, who was furious with his father for reducing his spending money.

Briana Ressner, a 40-year-old North Carolina chef who dated Gilbert in the summer of 2014, testified in state Supreme Court in Manhattan that Gilbert became angry when he learned his father, Thomas Gilbert Sr, was planning to withhold most of his allowance.

“He was concerned about getting cut off financially,” Ms Ressner said. “He was scared. He was upset.”

Prosecutors said Gilbert showed up at his parent’s Turtle Bay apartment on 4 January 2015, and shot his 70-year-old father in the head after the elder cut his direct deposits to $300 (£240).

But a defence lawyer, Arnold Levine, has argued that Gilbert has suffered from a slew of mental illnesses since he was a teenager and was not responsible for his actions.

The defence’s first witness, Dr Michael Sacks, a Weill Cornell Medicine psychiatrist, testified on Monday that he treated Gilbert for years and diagnosed him with severe compulsive disorder, depressive disorder, paranoid disorder and psychosis.

Gilbert’s paranoia proved the most troubling, Dr Sacks said.

Gilbert said in numerous sessions that he believed sketches on the NBC television show “Saturday Night Live” were about him.

“One of his delusions that he revealed to me: the belief that ‘Saturday Night Live’ for years had been making fun of him, and that he was thinking of hiring an entertainment lawyer,” Dr Sacks said.

Justice Melissa Jackson, who is presiding over the trial, has ruled Gilbert is mentally competent, which means the court believes he can understand the proceedings against him and is able to help with his defence. The judge agreed with the assessment of a psychiatrist hired by the Manhattan District Attorney’s Office, Dr Stuart Kirschner.

To prevail with an insanity defence in New York, defendants like Gilbert must prove that their mental illness impeded them from comprehending that they committed a crime or from knowing what they had done was morally wrong.

After weeks of being reprimanded by Justice Jackson for spouting random objections and nonsensical legalese, a gaunt and pale Gilbert, 34, has largely been absent from his own proceedings, choosing not to come to court on most days.

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Though Gilbert’s courtroom tantrums may have given the jury the impression that he’s mentally unstable, not everyone saw him as a mentally disturbed man in the months leading up to his father’s murder.

Two ex-girlfriends and his uncle described him in testimony as “shy” and “awkward”, but said they did not see signs of severe mental illness, nor did they think he was a murderer in the making.

The witnesses said Gilbert seemed more concerned with maintaining an easygoing lifestyle than following his father’s footsteps.

His father, who attended Princeton and Harvard Business School, went into finance and founded Wainscott Capital Partners Fund.

His uncle, George Seymour Beckwith Gilbert, a merchant banker living in Connecticut, testified that he had spoken to his younger brother about Thomas Gilbert’s lack of ambition.

He said he felt he had a right to speak up because he had paid for his nephew’s Princeton tuition.

“I said he ought to get a job,” he testified. “That’s the way we were brought up,” he added. “We always worked summers after we were 16. And we were expected to get a job when we got out of school.”

Yet the younger Gilbert seemed unconcerned with making his own way, his uncle said while trying to keep a steady tone of voice. He said his nephew did not reply to emails that included suggestions about job opportunities.

Instead Gilbert asked his uncle for a recommendation so he could join the Devon Yacht Club, an upscale social club in the Hamptons. He already frequented both the Maidstone Club in East Hampton and the River Club in Manhattan.

Asked by a prosecutor if he knew why his nephew struggled to find work, George Gilbert replied: “No, I’m not aware of any reason why he couldn’t get a job at the time.”

Thomas Gilbert appeared equally aloof and cold in correspondence with his parents.

In emails, which were shown to the jury Monday, he asked them for money to pay for gym memberships, clothes and to get into charity events.

But once he got the funds, Gilbert rebuffed their invitations to get together.

“Again, I requested no emails,” he wrote to his father after being asked to attend one event. “Please stop, so I don’t have to change my email address. This is a form of harassment.”

Gilbert dabbled with the idea of working at his father’s hedge fund and even spoke of starting his own.

“It seemed to me he didn’t have experience to do that,” said Anna Rothschild, 53, a publicist who dated Gilbert in 2013. “He didn’t seem to be highly intelligent, in my humble opinion.”

Ms Rothschild testified that she found Gilbert “odd”, but continued to date him because “he was very good looking”.

Ms Ressner said she regularly found evidence that Gilbert was seeing other women while they shared an apartment: fingerprints on a bedroom mirror, an unexplained box of condoms and even strands of other women’s hair.

“He didn’t bother to clean up when I came back,” she said rolling her eyes. “I did not have self-esteem at the time.”

Prosecutors have presented evidence of sinister intentions in Gilbert’s web browsing history.

In October 2014, he searched for “Hitman Services” and “Murder For Hire”, according to evidence the jury saw on Monday.

Gilbert’s uncle said his brother never imagined he might someday be killed by his son.

“My brother was always very positive — he was an optimist,” George Gilbert said. “This is sort of a bad dream.”