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The two pink wires on the ignitionswitch are probably reversed, note: only the two pinks, not red or any other. If you check a little further, you will probably find that the gauges and radio also have power with the switch off.
The initial problem was likely that the 18P, which feeds the Flasher, was plugged into the BAT terminal on the Ignition Switch. (Note marked VACANT in Dave's photo below)
The 14P is for the Gauges, Radio, Heater circuits.
18P should go to the IGN terminal(spare terminal)
14P should go to the ACC terminal.
Internally, IGN on also feeds power to the ACC terminal.
The original position that your pink wire for the gauges was most likely correct. If you can put it back where it was and then move the other pink wire to the position shown in the picture, you may be ok. Use the picture and check all the connections for the proper location. The pink wire marked 18P in the picture will be the smaller of the two wires, so you can tell which one goes where. It goes over near the brown wire in the connector.. Make sure the larger pink wire is on the terminal marked "acc" when you're done. And as rich said in the post above, nothing should be on the lug marked "vacant" which electrically is the same point as the red wire and is always hot.
I think rich5962 nailed your problem, I didn't take into account the extra lug when I advised you to switch the two pink wires. You really only needed to switch one, from the "batt" to the "acc" lug.
Other than incorrect wiring, the only other explanation I can think of is a switch that is defective internally, and that is not a high frequency failure. Post back what you find when you check the wires against the picture.