The only starter motors that will run backwards with reverse polarity are the ones made with permanent magnets instead of field coils in the housing. That didn't begin until the mid-1980's when the manufacturers got on a weight-reduction crusade.

If the solenoid is hammering in and out as you hold the key in the start position, you have a bad "hold-in winding" in the solenoid. Unless the starter is fairly new and in good condition otherwise, just swap starter, solenoid and all for a rebuilt unit. The cost won't be much more than a replacement solenoid.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!