It isn't the case of "enough resistance", its a case to too much resistance. The mechanical flashers have a bi-metallic strip that heats up when current is flowing (while the lamps are on). When the strip gets hot enough it bends and the circuit (contacts) opens stopping current flow and turning the lights out. The strip cools and straightens out the bend. The contacts touch again and the whole process starts over again, about once a second. When there is too much resistance (like when one of the bulbs burns out) there isn't enough current flow to bend the bi-metallic strip, so no flashing. Same when low current (high resistance) bulbs (like LEDs) are installed.

Solid state flashers don't depend on a bi-metallic strip to open and close the circuit. It switches the circuit on and off electronically. Many require a separate ground wire.

'57 GMC 102, Original 347 V8, HydraMatic, 3.08 rear gear, added A/C, disk front brakes, HEI, AFB carb, '98 Honda Black Currant paint. T-boned and totaled 10/12
'52 GMC 152 Stake Bed, Original 228, SM420, added A/C, HEI, disk front brakes, '67 Chev 3.55 rear gear. Gets used as a real truck.