1998 Cadillac EL Dorado Oil Pressure Light

I work for a GM dealer and very recently did the dreaded head gasket job on this Eldo. Runs fine now but on the initial test drive of approx. 15 miles, stopped at a stop light and the oil light came on in the cluster. I raised the rpm's and it went away while sitting at the light. Went to next light, same thing except this time the message center said "low oil pressure, stop engine", so I did. Light changed and I restarted and took off, no lights no message. The engine never knocked. Since then I have made the same trip with no ac on and no oil light appeared, made same trip again with ac and it came on.

My question is this.I bought a cheap low powered battery. Is it possible that there isnt enough battery for all the electrical that a Cadillac has and after a lengthy drive, the battery isnt enough and makes the oil light come on? I monitored battery voltage and at idle it is near 12 volts, which is low. Could this cause the oil light to come on at idle, where there is less battery voltage and lower oil pressure?

Thanks