Rolled Ranger is correct.
A very simplified explanation (without too many technical terms) is:
incandescent bulbs work by resistance heating a filament in a (near) vacuum. LED lights work through physical reactions. LED lights have less resistance than incandescent bulbs. The flasher is heated by left over resistance that the bulb doesn't use. The LED bulbs "use" less resistance so the flasher gets more resistance, which causes the flasher to operate faster or not at all.
The solution is to get a flasher designed for LED bulbs. The LED flashers don't rely on resistance to operate, and can operate incandescent bulbs on the same circuit. They are more expensive, though.
Actually you got the idea right but the electrical theory wrong.
Current flow is inversely proportional to resistance.
So something that draws a lot of current (Amps) has a LOW resistance, and thus more current flows, because more current flows and the voltage is available to maintain that current flow power is consumed (watts).
LED's actually have higher resistance, lower current flow and use less watts.
But the electro mechanical has a bi-metallic arm inside a relay that is wrapped with wire, when more corrent is drawn through the flasher that wire heats up, the bi metallic arm warps, and this cause the contact to open (you can hear a distinct "click" when this happens.
Because LED's don't draw enough current the metallic arm doesn't heat up as fast (or at all) and the flashers either flash really slowly, or really fast OR they don't flash at all.
The "fix" as mentioned above is an electronic flasher that uses an integrated timer circuit to control the flash rate rather than a thermo mechaical device.
Electronic flashers are necissary if you tow a trailer because the extra load from the trailer lights change the flash rate...
While I use an electronic flasher I sorta side stepped the issue as well, because toe only thing getting power at the back of my trucks that isn't run off of an isolating relay is the backup lights.
For the markers lamps, brake lamps and turn signals are on relays under the hood in their own little enclosure (robbed from a 1996 Explorer)
I am not the least afraid to "cut into factory wiring", if I were I would've never swapped a 4.0 into my '87...
But more on topic with lighting I would not now have all Wedge-base bulbs in the "Corners" of my truck.
I spent an entire weekend replacing my taillight harness and front turn signals.
AD