If your relay were bad, it would fail in the mode you would have if the button were "ON" and the lighted arrow pointing upward should be ON meaning overdrive would be OFF. I know that arrow light seems bass ackwards, but that's how it is. If you can gradually speed up to 55 and do not see the tack drop back three times (1st-2nd, 2nd-3rd, 3rd-overdrive) then your overdrive is not engaging. (also search for a recent post where someone was asking about what RPMs to expect at highway speeds in a 740T.) It sounds like the up arrow light in your car may be burned out because if it ws just that your overdrive unit was non-functional, the light should still come and go with the switch and if your relay were just bad, your light should be on all the time. Turn the key to the run position without starting the car and push the switch. If your relay is moving, you should hear a click from the center of the dash.

As Aleekat says, the best info about how this all works, where the relay is, etc. is in the FAQ under LINKS at the top right of this page.
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Andy in St. Paul. '89 244 160K mi, '91 745 209K, '91 745 213K