Ammeter waving when ignition is on.
I only know '67 well. In '67 the wiper switch is also used as a junction for powering the reverse lights.
So it could be the switch, the wiper motor - maybe its shutoff after one more sweep function, or the reverse lights.
Before going further will need to know which wiper setup the car has, and which backup light switch setup it has.
Fixed
Well you're somewhat in luck. The electrical diagram in the '68 FSM is more complete than the '67. There still might be several wiper switch versions for 2 sp, 3 spd etc.
I only know '67 well. In '67 the wiper switch is also used as a junction for powering the reverse lights.
So it could be the switch, the wiper motor - maybe its shutoff after one more sweep function, or the reverse lights.
Before going further will need to know which wiper setup the car has, and which backup light switch setup it has.