Through the first half of the season, the Red Sox were in first place with a half-game lead over the Yankees, and a staggering 54 victories, but they’re far from perfect.

As the second half begins, one need for the team seems to stand out above the rest, and that’s bullpen help.

Short of a potential trade deadline move next month, the Red Sox don’t have a lot of options, but one name continues to loom: Tyler Thornburg.

After getting surgery to treat thoracic outlet syndrome in his right shoulder, the right-handed reliever has been on the disabled list since the beginning of the season, and his return date has continued to be a mystery during what’s been an up-and-down process.

Thornburg began his first rehab stint on April 30, and he appeared in nine games before he was shut down. His second rehab stint began on June 2, and the 30-day window ends next week, when the Red Sox will have to make a decision.

It’s unclear just how close Thornburg may be to returning. Before this week, he hadn’t pitched more than one inning, and he still hasn’t pitched on back-to-back days — which are both necessary precursors to his return.

Thornburg needs not only to be capable of both, but be effective, and on Wednesday, he wasn’t necessarily that. He pitched two innings for the first time this season, with Double-A Portland, and much like this process, he was inconsistent. He gave up two hits, including a home run, and struck out three.

Physically, it seems that it at least passed the test for manager Alex Cora.

“He feels fine,” Cora said. “He’s going (tomorrow) again. Hopefully he can bounce back from this one and go (tomorrow). He’ll be back with us Sunday and then we’ll go from there. The reports were good — velocity, windup, everything. We’re pleased with the way he went about it.”

The next test, as Cora said, will be tomorrow, when he pitches with Triple-A Pawtucket. How he performs there should go a long way into figuring out the unknowns — when he finally may be back — and how much help the Red Sox will ultimately need in their bullpen the rest of this season.

“It’s been that way the whole process,” Cora said of Thornburg’s roller-coaster rehab. “He has a good one, a bad one, a good one, a bad one. The way he feels, this year he feels great. Hopefully (tomorrow) he goes out there and feels right and he bounces back the way we want him to, and himself, too, and we’ll go from there.”