Replace the cables and clean where they attach first.

 

And swap the starter relay with the horn relay. See if anything changes. If not, replace the starter.

 

A knowledgeable older guy at a parts store tested my electrical system and said it was good and guessed that the starter is wearing out. I will let you know what I find.

 

Should be able to do a draw test on the starter at the parts store..... See what that looks like.

 

I will check with the parts stores.

When I said it "clicks", I should have said it clicks once with each turn of the key, not the continuous clicking that one hears when that battery is dead.

 

It is a light click, or a heavy one? (starter motor, or relay??)

 

Click indicates that either there is something wrong with the power supply (loose or corroded connection, even a bad battery), but I would bet my money on worn out brushes. Solenoid does pull (click), but when the brush worns out, it gets hung up on its holder, creating no connection issue. There's just some sparking between the brush and commutator. I've made temporary fix in this situation and filed off some material so the brush doesn't rest against the holder.
Other thing that creates 'click' situation is when the solenoid contactors and plunger plate burn, and that burning forms spikes to those parts creating uneven surface which does not conduct enough electricity to turn the starter armature.
Sometimes you can get away with clicking starter by tapping it with a hammer.

 

I have not replaced a starter since the eighties and do not recall what prompted starter replacement back in the day and that is why I ask now. Did they suddenly stop working? Back in the day, it seems we were always visiting salvage yards and pulling parts. I also recall pounding starters and using a screwdrivers to start the engine. I have no problem replacing this unit after 175000 miles as I am pleasantly surprised that the engine still runs and uses almost no oil. The only non-original parts on the truck are the water pump, plugs, distributor cap, rotors.

 

Please disregard the attachment.