Dash cluster Signal indicators

Seems to me that the two 1157 bulbs along with the fender mounted would be enough load to operate the flasher. I have driven a 67 without its inst' panel and the signal flasher did work. That model doesn't have the added fender mounted either, so my 1st suggestion... a new flasher wouldn't break the bank.
If that doesn't cure it, check for good 12 volts into the flasher and check the chassis ground paths at all exterior fixtures from inside wall of bulb socket to battery neg'. You might have stumbled onto a weak exterior lighting issue that was already present. We've seen cases where flasher didn't work at switch on/battery alone but would work with engine running/alternator output.
In the end, If you still need the additional load of the #158 indicator bulb to operate the flasher, the very low load of LED probably wont get you there.