MikeT,
Possible causes:
1) Check the bottom of the tank to see if it is dented, causeing the sending unit to send an improper fuel level reading.
2) Faulty fuel sending unit, You are actually below 1/8 tank. (My S-10 has this exact problem also @1/8 full reading. I opted for Patmans solution, since I am too lazy to drop the tank and replace it.)
3) Baffle in tank has come loose, allowing fuel to "slosh" away from the pickup when a low fuel condition exists.
As for the primary fuel pump ... Turning left or right should not effect it's function/performance. A bad primary pump is usually associated with a hard/long start condition.
Since you say that it ONLY happens once the tank is down to 1/8th, I would not think it is an electrical problem.
Hope this helps,
wrench