??? My 65 had neither a toggle switch, nor a plug, nor a hole there originally. I did put a toggle switch there in the early seventies for the driving lights I was running at the time. Now have a toggle switch hooked to nothing, just to plug the hole. Things have been added to these cars in the 57 years since they were built. I don't think the switch in the picture is factory, but every now and then I find out about something that was rare when new, but did exist. So ???
I have a plug there on my '65 convertible (never saw it on the hardtops), so I assumed it was a factory hole meant for something. Still waiting for someone to chime in with a definitive answer.
From Ross Roy, looks like 65 Barracuda optional equipment included an emergency flasher and a rear window defogger, both dealer installed. I could see a switch for either of these options having been placed on the left side of the dash. (Where else would you put them?) Since these options would have been dealer installed, I can also imagine some variation in exactly where the switches would have been placed. (I note that your plug is not quite in the same place as the switch in the top pic.)
That position was usually for a power convertible top switch. I guess they could have put the optional flasher or defogger switch there too, but, the ones I've seen were mounted down a lot lower on the dash.
Looks to be convertible top switch. Can’t tell on my phone but if the a-pillar interior trim is chrome it’s a convertible
Interesting that the top switch and the black plastic bezel around it (with white lettering) is in the style of 63-64 dash switches. It doesn't match the 65 Valiant/Barracuda switch style at all. Guessing that Chrysler didn't want to bother tooling up for a top switch in the 65 style for the limited run of 65 Valiant convertibles.