When you resoldered all the terminal on the original relay, you got it working right. Unlike some cars, the 144 indicators do not light up when the emergency flashers are on. The only indication you get when the emergency flashers are on is the illumination of the hazard switch itself, in unison with the four external blinkers. Some 244s have the switch and the indicators on the dash illuminate at the same time when the emergency flashers are on, but not on the 74 144.

If you turn on the turn signal and the green light in the dash does not illuminate, it could mean a blown or mismatch bulb, or a bad ground. Might want to check that out.
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...and the bricks keep on rolling