The 94 truck and Blazer both use the Saginaw column, and the switch inside works like this.
Power from the fuse box goes through the flasher then into the turn signal switch to be routed to left or right bulbs, at which point if finds the ground after the bulb. The ground on the blazer is after the little 194 bulb in the amber lens beside the headlight, so if that bulb is burnt out you lose your ground. And that can cause this. Broken ground in the front effected side. The rear gets a ground on the left side frame for both sides.
the hazards since they run on a similar designed circuit, but will find a ground from both the left and right front, they will prolly work. Another thing to consider is the switch itself, as the wiper contacts for the right side may be worn out. Since the hazard part of the switch is slightly different, it may still be making good contact.
honestly, check the grounds, and make sure the little 194 bulb is good if you have one. And yes this is possible that the little bulb in the front can effect the rear, as there may not be enough current to activate the flasher which relies on current flow to trip and reset.