I have a 97 f350 with the 7.5L gas engine and it's been sitting for awhile and I'm trying to get it to start but it's just clicking and plummeting the battery meter. I added a couple extra grounds but same results

 

If I understand correctly the symptoms you have described, Would be a good move to remove all battery cable connections , clean them and reinstall.If there is no change then make sure the relay on the fender well is getting good power to it.Depending on how that relay gets it's ground, which sometimes is through the sheet metal of the fender well. Those fender wells can get pretty rusty and don't have a good ground to have the starter relay close well enough to make good contact and send battery power through it on to the starter. Sometimes a light blow to the starter may allow the brushes to move down and make better contact. The best way to confirm battery cable integrity is to do a little voltage drop testing to make sure there is no internal corrosion..

A simple test you can try,
Turn the headlights on and attempt to start the engine. If the lights stay bright there is a starter problem. If the lights go dim ,poor connection or weak battery