The stock flasher unit is sensitive to voltage and load conditions.
Stock front bulbs were 1034 and are often replaced with 1157, which is higher wattage.
Rear bulbs were 1073 and are often replaced with 1156 which is higher wattage.
Changing bulbs changes the load condition on the stock flasher unit.
Next is voltage sensitivity. The stock flasher operates faster as the voltage increases.
When engine is stopped and electrical load placed on battery, the system voltage lowers.
It also matters if the battery is at full charge. And, turn signals seldom matter (operationally) if the engine is not running.
Even if the battery is full and the engine running, revved, the voltage to the system can be low if the connectors switch contacts, and fuse clips have oxidation/added resistance. The voltage loss increases with the current flowing through it. So, having a higher load like the headlight on will induce more voltage loss on the black wires in the harness which powers just about everything. Don't forget ground connections, as they are part of the current loop out and back to the battery.
Many don't wish to go through the electrical system and clean the switch contacts, polish fuse clips and restore the connections to low loss connectivity, and simply replace the flasher unit with one that is insensitive to the system voltage levels (not stock).
I prefer the original, as the flash rate tells me if the system is charging and gives a battery health indication in the process, without adding a voltmeter. It can also indicate when attention to voltage distribution components is warranted.
Cheers,