It sounds like, if your sending unit and gauge are working, you might have some corrosion or a short on the wiring for the warning lamp causing it to glow. Before you replaced the sending unit, when you say the warning lamp would come on, are you saying it would light up fully, day or night, more than just a faint glow?

1989 Dodge Raider V6
2001 Jeep Wrangler 4.0L
2008 Toyota 4-Runner SR5 4wd