Just bought an 88 F-150 with a 4.9L. PO starts the truck with a screwdriver by the solenoid. There are 2 wires that has the L-shaped connector (secondary). One seems to be OEM. The other seems to be jimmy-rigged.

I put a volt meter on any one of the L-shaped connectors and it shows 7.68VDC in position 2 and 3 of the ignition. Is this normal? Shouldn’t I get 12VDC at any one when I try to start the truck at ignition position 3?

 

Do you have two small terminals on your fender mounted relay? If so, one should be marked "s" and one should be marked "I". Disconnect the wire going to the "s" terminal and test it to ground. When the key is in the start position, you should have 12 volts to that wire.
Disconnect the wire going to the "I" terminal. With all other wires connected, and the key in the start position, you should have 12 volts at the "I" terminal when tested to ground.
The "s" terminal gets it's voltage from the steering column mounted ignition switch, and the "I" terminal is energized with your starter when the key is in the start position.
I'm not sure your truck came with a 4 wire relay, so someone may have modified it.

 

All your truck's details need to be in your signature as this page explains so we can review them with each reply:

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There's also a link that explains how to add pics to your posts so we can see what you're seeing. When measuring voltage, it's critical to know where EACH of the meter's probes are, in addition the positions of all the relevant switches.

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But Ford doesn't number the ignition switch positions. Read this page:

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This page describes the starter relay terminals (the solenoid is part of the starter, under the exhaust manifold):

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Soupbean
S is for Start - not switched.