During a brief exchange between Brooks, Julie Hagerty, and a motorcycle cop (that ends with a ticket being avoided due to a mutual appreciation of EASY RIDER), Brooks says:
"Did you see THE TERMINATOR?"
–"No, I didn't. Heard about it, though."
"You should see it. You look like him."
Now, since LOST IN AMERICA was made in 1985, Brooks must be referring to Cameron's original TERMINATOR (from 1984), drawing a humorous comparison based on the cop's demeanor and sunglasses, comparing him to Arnold Schwarzenegger's titular character. However, while the cop doesn't actually resemble Arnold in any meaningful way, he is a dead ringer for Robert Patrick's motorcycle cop-impersonating T-1000 in TERMINATOR 2: JUDGMENT DAY...
...which was not released until six years later, in 1991. So maybe James Cameron was watching LOST IN AMERICA when he decided he needed a motorcycle cop Terminator? Or perhaps Brooks is referring to Patrick, whom he glimpsed in a time-traveling VHS copy of TERMINATOR 2. (Which must have been the splitting point for the Berenstain Bears parallel universe.)