I don't know the resistance range of a TR4 sending unit, nor do I know when in history the voltage stabilizer was added to Triumph gauge systems. There is a very good chance you can use the AutoMeter gauge if you make some measurements to help you select the right gauge.
There are several common resistance ranges used by OEM and aftermarket fuel gauges. What you need to do is determine the range of the sending unit in your car and buy a gauge to match. The terminals on the sending unit are probably not easily available to you but if they are... disconnect the wires there and connect an ohm meter across the sending unit terminals. When the fuel tank is almost empty, use something through the tank's filler neck to lift and lower the float arm. Record the resistance with the arm up (full) and with the arm pushed to the bottom of the tank (empty).
If you can't access the sending unit terminals, your only other choice is to access the sending unit wire behind the gauge. This will probably be green/black. Disconnect the wire from the gauge and connect your ohm meter between the disconnected wire and chassis ground. Perform the arm lift/lower resistance measurements as described above.
Once you know the resistance range your sending unit operates through you can select the proper AutoMeter gauge. They should have several to pick from. The most common ranges for British cars are 0-90 Ohms (empty to full) for MOST cars made without the voltage stabilizer, and 240-30 Ohms (empty to full) for later cars with the voltage stabilizer.
Sorry for the long winded reply.