Hi there -(somehow my response was missing a huge portion)
(screwed up again. One more edit)
Adding flashing can be done by wiring a flashing module in series with the power, just like the switch.
The decision is to build or buy. I hinted at this above, when I suggested using a BJT/MOSFET in the switch location, driven by electronics. You could build a 555 based timing circuit to drive the transistor switch.
But, I suspect that this may be a strain on your skills. Even if we supply a solution, can you read a schematic, wire ICs, transistors, resistors, capacities and relays? Even simpler, can you solder?
Or, you can buy a flasher module. One which has selectable patterns and is used to drive LED lights, can cost you $30-$40. Or an automotive flasher relay used in turn signals can be used at a cost of $10-$20. If the flashing rate is acceptable.
The ultimate solution which you can ignore is microprocessor based. Someone else may suggest it, but then you add on a learning curve for programming and uploading your program. I don’t recommend this solution for you.
If any of these ideas appeal to you, let me know. Then I can provide more detail.
Thanks for this thorough explanation. You're right to presume that reading a schematic would be beyond my skills. I am essentially looking for the simplest possible solution to the problem. The most I can be expected to do is to solder 2-4 wires to clearly marked connectors. Aside from that I'm looking for a set of devices with clearly marked "input" and "output" cables that transform an electric current into blinky lights