I have an old truck with a dead instrument regulator like yours. I tried making a regulator using a 7806 and a heat sink. I also tried the LM317. They almost worked. Some of the instruments worked well and some did not. They were off a little in the readings. The original regulator, at 12 volts is on 50% of the time. Some of the instruments are OK with 6 volts and others needed the 12 volts at 50%.
I ended replacing all the old instruments with new ones and new senders. The new instruments do not need a regulator. They work from 12 volts. They look just like the old ones (if you black out the name).