555 auto-off timer circuit validity
If you had a resistor tied to the battery only, yes less current would be driven by that 1 MOhm resistor, but actually less heat is generated. Heat is generated from the power dissipated (as heat) by the part. So power is V * I which is (for a one resistor, one 12 V battery setup) 12 V * (12 V / Resistance) using I = V/R to calculate I. So as resistance goes up, power goes down for a constant voltage. 

I don't know enough to reliably help you with your main problem, just thought I would contribute what I could.