88 Jeep Cherokee, left turn signals don't work. Right signals flash as they should. Emergency flashers work as well. When the left turn signal is activated, the dash arrow lights up, the front bulb lights up and the rear bulb lights up but the flasher doesn't click. The flasher was replaced to rule it out and because it is easy, the left rear turn signal bulb was replaced and the front bulb was checked. It seems to me then next item to replace would be the turn signal switch. Any thoughts?

Quite a puzzle you have that seems impossible, though such things weren't unusual in the old days of bimetal flasher units. The modern electronic flasher relay is designed to flash at a speed dependent on the amount of current drawn by the circuit so if a bulb goes out the speed doubles or thereabouts, giving the driver an indication something is wrong.
Broadly speaking the flasher unit will operate as it is designed within a current range so if there is too much current flowing or not enough it probably won't work at all.

The turn signal switch is usually a very reliable thing and as the left hand lamps light it is fair to assume it is working ok. If the switch is accessible it would be simple to measure the current being consumed by the circuit, which would be nearly 4 amps with the engine running at a fast idle. If it isn't then I suggest you revisit the lamp grounds and other connections.

My instinct is to suspect the hazard warning switch. It is often an unnecessarily complex switch and wiring arrangement and often responsible for turn signal malfunctions. Mostly operating the switch rapidly for a few minutes puts matters right, though if it doesn't I suggest you check the multiway connector behind the switch.