Stalling question, sort of odd..

Well the turn signals are a totally different circuit so I don't know any way they can affect it running. You can even unplug the turn signal plug an it'll run fine. But what the heck, wiggle them too just to make sure. I wouldn't be surprised if you don't eventually have problems with the turn signals too (which also control the tail lights) due to the butt connectors. Butt connectors were designed to be used as a temporary repair, not permanent. To do it right the wires should have been soldered at the splice and shrink wrap or a high quality electrical tape used to insulate them.

If wiggling wires under the hood doesn't do anything also try wiggling wires under the dash as there are also wires there that can stop it from running. Especially the wires near the ignition switch. You might even try jiggling the ignition switch as they go bad also, although they don't usually cause the problem you have of it dying when you back up but you just never know.