One of a few problems with the relay gone is your cause.

Incorrect wiring under the auto.

A solenoid that has fluid inside combined with poor actuating piston seals. Sounds doubtfull at this point.

A broken pressure control spring combined with a solenoid problem.

Symptoms as you describe seem electrical and are also the easiest to eliminate.

To eliminate the wiring problem, under the auto, at the OD, remove the power feed terminal from the solenoid, tape over it to prevent electrical shorting to anything else and then tape it to the ground wire loop to keep it from getting torn off as you drive. Or trace the wire back to a connector (it may be inside)and remove it from under the auto completely.

IF this "cures" the OD shifting in and out of its own accord, you have gained some time for correcting the previous owners attempts at getting the OD to work without the shift knob button. Basically, a circuit trace and repair, correcting the connections along the way until restored to factory specs.

IF with no power to the solenoid the OD still shifts in and out, more diagnostics are required to pinpoint the cause. This also increases the need to correct as soon as possible. An OD that can self engage without an electrical connection increases the chances of self destruction while using reverse.

Shifting in and out without using the clutch is not good for the OD but over a short period will not increase wear and tear significantly. It would be wise though until this self engagement is fixed to refrain from backing up if at all possible. If you do back up, get rolling and coast as much as possible with the clutch in. Keep it slow without much power.

Duane