84 has an internal fuel pump. A quick check is to remove your air filter. The metal box behind it connected to the tube to your intake is air flow meter. There is a flapper inside that you can move easily. With the ignition on, stick something in the flap to hold it open. This will cause the fuel pump to engage and you should be able to hear it.
There is also a test lead there that can be jumpered to engage the fuel pump.
This is the link to the Technical Service Repair Manual (TSRM) for the 1986 MKII. Your 84 is not significantly different. It has a wealth of info and detailed instructions for testing.
http://www.cygnusx1.net/Supra/Library/TSRM/MK2/