To expand on TOOLS, these old mechanical flashers require a load. Even newer solid state flashers are thermal. So, get a new, 2 prong flasher, a 3 can work too, 1 tab is just unused, that works with LEDs. OR you just shot yourself in the foot and wire in a resistor to each unit to increase draw to trigger the flasher. This is dumb in my book as part of the idea behind LEDs is to lower draw.
Also, the headlight issues is simple. A halogen pulls more wattage than the old sealed beam did. This makes the flasher slower, most noticeable at idle. These systems do not have much extra wattage to spare. SO, go through all your wiring and CLEAN every connection. Dirty connections cost a LOT of voltage. Bad connectors should be replaced. Any connector not needed, should be removed and the wires soldered. Replace that old fuse block too, with a new blade style holder.
Also, make sure your regulator, if original, is adjusted right.
The ride IS the adventure. The destination is just to get gas!