All true
@Andrew Shadow , replacing the relay is the best, but not the only solution for the rapid flashing. That happens because in older, incandescent lighting the resistance of the bulbs is part of
an RC a circuit that uses a bimetallic strip whose changes in temperature determines the flash rate and the filament of the lamp is part of the resistance in the circuit. A load resistor can be installed across each LED lamp to flash at the usual rate with a conventional flasher.
The forgotten advantage of the solid state relay is that it flashes at the same rate with either LED or incandescent lamps. Should one of your LED lamps fail, you can install a conventional incandescent lamp as a stop-gap and everything will still flash at the same rate.
Edited to remove incorrect description of an RC circuit in the conventional flasher.