Is there a cable or sensor on the odometer for 1992 tercel

They both work off of the same cable, so I would say that you have a problem in the speedometer head itself and will need replacing or sent in for repair.

If it has a speed sensor it is mounted in the side of the transmission where the speedo cable would have been.

The sensor is usually located at the passenger side axel near the wheel drum. It works by sending a signal to the PCM at the exact velocity. I think it is the sensor.

I believe a toyota blink code 22 is " Engine coolant temperature (ECT) sensor open/shorted "

Code 22 is the Water Temperature Circuit Open or Shorted.
Fig. 1: Trouble codes for 3E engines

Fig. 2: Trouble codes for 3E-E engines
Fig. 3: Trouble codes for 3E-E engines

Is the check engine light coming on? If so your o2 sensor may not be working right because of the bad exhaust problem? Change distributor cap also. Check timing. Hope some of this helps.

speedo itself?

INSPECT YOUR SPEEDO CABLE, IS IT BROKEN?????, IF NOT THEN IT'S YOUR SPEEDO HEAD BROKEN....IF YOURS IS ELECTRONIC THEN CHECK THE SENSOR AT THE TRANS "VSS" SENSOR...WITH OUT TEST EQUIP. JUST REPLACE IT AND RETEST.....gl

find a way to get to the switch in the rear hatch and try diconnecting the switch.

check the vehicle speed sensor located on the transmission housing.