Update on October 2: William Gomez and his two children have been found safe in Wisconsin.

Original post: William Gomez drove away in his family's white Jeep at about 2 p.m. Sunday with his two grandkids, 7-year-old Marcus and 8-year-old Dominique, ostensibly headed for Carrollton's Rhoton Park or Lewiville's Vista Ridge Mall.

Family members haven't seen them since. They contacted police that night after the trio failed to return home.

Carrollton PD issued an alert on its Facebook page, but it soon became apparent the kids probably weren't going to turn up locally. Early Monday morning, Gomez' debit card was used in Little Rock, Arkansas. That afternoon, it was in Troy, Tennessee. Still later, and still further from home, surveillance video showed him buying kids' underwear from a Sears store in Paducah, Kentucky.

Police say that Gomez never meant to wander out of state with the kids.

"Mr. Gomez has a medical illness that causes memory loss, so we're very concerned for him and also for the children," Carrollton PD spokeswoman Nicole Rodriguez told NBC 5.

His wife, Maria Gomez, tells CBS 11 that he stays home most of the time as a result.

"He had a tumor 10 or 12 years ago, and that's the cause of his buildup of the fluid in his brain. And once in a while he gets like this," she said. "Most of the time, he's OK."

For now, he's not, which has family members worried. Family members suspect he might be driving to New Jersey, where he was raised. But he asked the Sears clerk in Kentucky for directions back to Dallas. Maria Gomez doubts he'll follow them.

"He's stubborn that way. Even though he may think he's lost, he'll keep driving straight," she told WFAA.

Update at 12:11 p.m.: Make that Chicago: