Why would the intermittent wipers not work but low and high speed of the wipers work?

The wiper circuit that controls (in this case that opens the ground circuit of the motor)the motor is staying closed to ground...it needs to be open when in delay mode...so that the delay circuit can control the opening and closing to ground. OR the delay circuit has an open circuit...burned up capacitor, relay, etc. Or it could be a stuck parking switch...which should open on in park mode...however the wipers would stay on until you turned off the wiper switch. Also, old cars up to 1980 or so...used ground type switches whereas new cars use powered switches and relays to latch the motor to ground.