Wiper quit on 99 signature series ford

hi think you need a new motor as the control module is built into the wiper motor

This is (obviously) a two-speed motor. The low speed winding is burned out. Replace the motor.

Lift up once: results in one swipe

Pull down to position 1: results in intermittent wiping

Pull down to position 2: results in constant slow wiping

Pull down to position 3: results in constant fast wiping

the wiper moter has a module on it and when they go bad it will do what yours is doing. i would replace the wiper module and it should fix it.

Somehow the rheostat has burnt out--will have to remove & replace--probably a garage job.

you need to replace multi function switch

Sounds like your intermittent wiper circuit is defective. Normally the intermittent feature is engaged by one of the functions on the multi-function switch (usually on the steering column). The circuit of the intermittent wiper periodically activates a relay that closes across the "Wiper On" switch. Your intermittent wiper circuit is likely defective and holding its relay closed (or the relay is stuck closed), thereby keeping the wipers on. Note: The wiper motor has an internal switch that opens when the wipers are in the park position and that is designerd to stop the wipers in the park position. When you turn on the wipers (or the intermittent relay is closed), the motor's internal switch is shunted such that the wiper does not stop at the park point of the cycle.

the most common cause of this is the wiper switch.

The common way of controlling wiper speed is to use a 'tapped' resistor that supplies reduced voltage to the wiper motor on all but the fast setting.
They have to dissipate a good bit of heat and are subject to failure; I think yours has done that.