What weight oil are you using? Try 10W30 or 10W40 if not one of those.

I just filled up with Mobil1 10W30 in order to use up my remaining stock. I watch the oil pressure in all my cars like a hawk. Here is what my T does:

Starting up cold oil pressure immediately jumps to the middle of the gauge at idle. As the oil warms, after 30-45 minutes of driving, it's now thin enough to idle near the line above the L mark. I estimate this is about 7psi.

Cruising between 2k-3k rpm the needle is always near the middle, further to the right when the oil is cold.

You got any valve noise? If you are using the right oil I would tend to think the meter or the sender may have an issue. Pull the sender off the block and hook up a mechanical gauge. You need to have at least 4 psi at idle and 36 psi or more at 3k rpm.