You can throw a control unit at it if you want, but you really should troubleshoot what you have first. If the blower works on high then we already know the blower relay is working and sending power to the blower motor. That power does not go thru the switch, it goes directly from the relay to the motor and the modes and fan speeds are controlled by the negative side of the circuit.
So if you look up the wiring diagram in the service manual for your 1999 over in the TJ Resources section you will see that the speed switch has 4 terminals, 3 of them send the negative thru the resistor block but the high speed terminal bypasses all of that and sends the negative directly to the blower motor.
So you either have a dash switch that is not sending that negative to the various resistor taps (which seems unlikely that all 3 positions would fail given the design), or the black/tan wire from the end of the resistor block to the blower is open, likely at splice 208.
Taking the dash apart is easy and also explained in the manual. A plastic trim tool/pry bar can help remove the console trim without damaging it once you remove the screws.
The diagram below is for my 2000 but I believe your 1999 is identical.
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