News:
With a good battery and good starter, when you short the relay terminals, than engine should crank till you remove the screwdriver. What do you mean it lasted less than a second? Make sure both ends of all battery cables are tight.
you are losing major voltage somewhere if you have 10v in the run circuit & 12v in the start position to the starter relay . start checking connections & the base of the column & bulkhead , you should be getting battery voltage everywhere
You have 2 small wires on the starter relay. If the yellow one has power when holding the key to the start position, then the other one isn't getting ground through the neutral start switch. Ground this terminal and see if the relay clicks. If it does then follow the brown wire all the way to the trans and check the switch with a test light.You need power and ground to make the relay close.