Oil temp sensor

Do this test:

1. (With the ignition key "on") Unplug the wire from the sender (107576) -- note gauge reading.

2. (With ignition key "on") Touch the (unplugged) wire going to the sender directly to ground (like the nearby bare engine) -- note gauge reading.

If the gauge changes from the "min" to "max" reading for the two conditions -- good sign for gauge/wiring/power and bad sign for sender.

If the gauge doesn't changes from the "min" to "max" reading for the two conditions -- bad sign for gauge/wiring/power.

 

Yes, no +12V is a serious problem that needs to be corrected. To test the oil temp gauge out of the vehicle:

1. Apply +12V to the "+" terminal on the gauge (the schematic shows there should be a little "+" symbol on the case of the gauge, and this terminal would connect to the VB, green-white, wire in the harness)
2. Apply ground to the "-" terminal (this terminal would be connected to the N, black, wire in the harness)
3. Also apply ground to the terminal connected to the oil thermistor (the schematic shows there should be a "C" symbol on the case of the gauge, and this terminal would connect to the M, brown, wire in the harness)

The gauge needle should go to maximum under those conditions.

If you don't have +12V on the VB, green-white, wire in the harness with the key "on", check fuse #21, but, if fuse #21 is blown, your speedometer/odometer shouldn't work either - do those work?

Not good. The oil temp sensor is a thermistor (not a thermocouple). Just to be sure that we are talking about the same thing, please confirm that the oil temp sensor you are working with is item 34 here:

https://www.ricambiamerica.com/car-diagrams/ferrari/v6-v8/328-group/328-1985/lubrication-system.html

 

That's fine for doing a test, but you're going to have to get fuse #21 to not blow as this runs a whole bunch of other stuff besides the oil temp gauge. If you don't have a copy, you can download the non-abs 328 wiring diagram here:
https://www.dropbox.com/s/vsxcnaheq1igub4/328%20US%201986%201987%20wiring%20diagram%20book%20440_86.pdf?dl=0
(If your 1988 328 is a very late 1988 with the convex wheels, give a shout and I can get a link up for that wiring diagram -- but, for the oil temp gauge system, they should be the same.)

The black wire in the harness is always connected to ground, but the brown wire in the harness would only be connected to ground if you connect it to ground at the end in the engine bay.

 

No, that's the speedometer/odometer sensor. The oil temp thermistor is located on the forward facing side of the engine oil sump and only has a single wire -- see the SPC figure link in post #4 - item 34.

 

Now that you are fondling the right gizmo, it sounds like you are making progress Now that you know that the oil temp gauge works, you can also make a resistance at the unplugged oil temp thermistor to better confirm/deny if it needs replacing. Don't quote me exactly on this, but, IIRC, the resistance measured from the unplugged terminal of the thermistor to the brass body of the thermistor should be something like:

at 25 deg C = 2K Ohms

at 100 deg C = a few hundred Ohms

So, if the resistance of the unplugged thermistor itself measured meg Ohms or infinite Ohms at 25 deg C = you know it's bad.