stupid ? of the day on Dana trac-loc

Ok I'm old and forgetful on a Dana trac-loc if one of the brakes
is locking more than the other one will that cause one tire to spin
and not the other when doing a brake burnout (automatic tranny)
Long story but I got lots of oil on the passenger brake and haven't
had the time to replace stuff yet I seldom drive this car

Time to replace the inner seals. I would do both at the same time.

It sounds like one brake is holding, and the other is slipping due to the gear oil on it.

If you want some fun, fix the seals and install a "roll control" AKA line lock.