1989 Volvo 740 Fuel Gauge

1989 Volvo 740 4 cyl 153000 miles

I bought this Volvo (1989) for my daughter, this is her first auto but the fuel gauge does not work so as a young driver I do not need her stranded over such a small issue. I changed the sender unit/ fuel pump thinking it would fix the problem but it did not. If I ground the (brown) wire that goes to the sending unit I get a reading on the fuel gauge but it is not accurate. I bought a book on this car but it does not tell me how to trouble shoot this problem. How can I test this system?