The voltage gauge is showing just over 12 volts but the voltmeter is showing 13.5. Could the gauge be faulty?

Normal. If you run a dedicated wire from the battery to the Gauge it will be the same reading.

Don't worry, your gauge is about as accurate as it is going to get. Not made with the performance of today's gauges. Remember these were cheap cars.

OK, thanks to you both

Have the same issue with a new VDO volt meter,I have a separate Hella fuse box I put in for any extra's,plan to wire the gauge direct to there.
I checked the gauge and its fine off a battery, appears to be reading 1.2 volts low.
I'am wired to the original centre console loom, guess the wiring too light and old to carry all the current.