What is the thread size on the back of oil pressure gauge??

The part of the gauge as pictured above uses a proprietary threaded nut to seal the compression sleeve. So it is absoultely beyond any reasonable doubt not 1/8" npt. The brass fittings in above photo are the nut,ferrule and the line adapter to engine block. Larger thread is 1/8"npt, commonly used on most early mopar engines.

A short line and adapter to your braided line is one way to connect it.
A gauge with a fitting that can be adapted would be a better way to go.

Honestly,who would want a potential oil leak in the passenger compartment? Go electric.

Absolutely correct. "Once you have" the 1/8 ferrule/ compression fitting, there is no fitting manufactured that will adapt to that. The only thing you can screw on there is the correct compression nut, unless you want to solder/ braze, JB weld, whatever.

"Mainline" traditional gauges like SW all had 1/8" pip so far as I know