Other solution for Frozen T Case Actuator?

[N4RNR]

Is it not possible to just remove the cover and take a screwdriver to gently move the gears and help it along, then bolt the cover back on? Seems like banging on the the cover is so indirect and it seems like taking the whole thing apart is overkill if it's just a little stuck (ie, worked recently).

Any thoughts on this, or is it not easy to just remove the cover then put it back without messing things up?

Thanks!