Mark is probably correct. [on edit] Jerry also got there first (as usual.)
Loose steering/suspension components could cause that. With a different load on those components with brakes applied, the steering geometry could be affected. A Model A I had would sometimes exhibit "death wobble", but applying the brakes would eliminate it. This would be similar but opposite. Maybe toe-in is changing enough with brakes applied to cause the wandering.
Last edited by klhansen; 11/18/2020 9:10 PM.