My 71 Pinto wiring diagrams dated 8-1-70 & 4-30-71 both show only one fusible link (a yellow wire) coming off the battery side of the starter solenoid.  The small red - light blue wire comes from the ignition switch via the auto transmission neutral interlock switch.  The small red - light green wire goes to the ignition coil.  The large wires go to the battery and the starter.  Of course these wiring diagrams may not reflect how your car was made, I suspect they made some revisions the first year.

Your symptoms sound more like a bad connection and/or a dying battery.  After the battery is "fully charged" and with everything turned off, measure the battery voltage at the posts (not the connectors) and it should be over 12V.  Having some one turn the key to start, the battery voltage should drop only 2 to 3 volts.  If it drops in half or worse, the battery has a bad internal connection and is in need of replacement.  If the voltage stays up reasonably well at the posts, move your measuring point to the post connectors and repeat.  Keeping moving down the string until you find where the big voltage drop is (could be more than one location) and fix.  Be sure to check the ground connection paths also.  FYI, I was estimating what good voltages are above and probably are not exact.