Furnace woes

As you can probably tell, I have an issue with an electric furnace. And, I don't really have anyone else to ask, except for you guys. Anyway, the problem I'm having is that the blower motor will not turn off. It doesn't blow heat unless called for so that's not an issue. But even with the switch on the thermostat turned to the off position it still blows. On the thermostat there is a three position switch on one side, heat, off, cool. And on the other side is the blower control lever with two positions. On and auto. I thought that it may be a sticking relay, so I put a new one in and nothing changed. The only way I can get it to stop blowing is by turning the breaker off.
I know it's an off the wall question but, I also know that there are some very smart people on here. If anyone could point me in the right direction, other than calling a HVAC guy, I would really appreciate it.

Thanks Tripod, I already stumbled upon this article. Believe it or not, I try to research before whining. Short of replacing the limiter switch, I couldn't find a reset on it. And I may have to replace it.Actually, from the time I had ordered the relay, to the time it arrived, the furnace started working perfectly again. But the day the relay shows up, the furnace started acting up again.
It's basically an analog thermostat with the mercury switch and all. I can see a little spark inside the mercury bulb when it calls for heat so I don't think it could be the thermostat. Who knows? I have the heat cranked up now so I shouldn't have to get up in the middle of the night to turn the breaker back on, lol.

Now that I'm up, I look into the thermostat more. It's a pretty simple thing, no electronics involved, but if I'm going to start throwing parts at this, it's probably the cheapest. The furnace people up here are hacks. If there was a burger joint up here, they would be flipping burgers at it. I'm not being mean, it's the truth.

I did replace a relay, and going by the furnace installation manual, it is for the blower motor. In fact, it's the only relay that I saw. The fan control on the thermostat only has two settings on it. Either on or auto. So maybe it could be the thermostat. Thanks for the input guys.

Quote from Jonathan Thompson

Disconnect the thermostat and if the fan goes off it's a bad thermostat if not than you know it's at the unit.

So I completely removed the thermostat and the blower motor is still running. But by my thinking, the furnace has to get a signal from the thermostat before it will shut off.and with the thermostat removed, it can't receive the signal. But you're saying that with the thermostat removed, the furnace should quit,right? I should say that the furnace isn't blowing heat now, but the blower is still running.

That makes sense. I've looked for a make/model but can't find it. I have the installation manual, and even then there's no mention of a brand. Would the switch you're talking about have a name? I'm starting to think that the new relay I put in is bad, cause for the life of me, it sure seems a relay issue.

Thanks for the offer D&M. I'll try not to call you unless I'm really stuck. I hate being a PITA. What I've read is it could be one of three things; a bad relay, a shorted thermostat cable, or a bad thermostat. Well the relay is new, the cable looks fine, so I guess I will try the thermostat.
I told my wife that I had posted this furnace question on this forum and she thought that I had slipped a cog. I told her that if anyone could help, that it would be you guys on this forum. I'm finally right for a change! Thanks for all your help, I knew I could count on my Slingshot family! Y'ALL are a great bunch.

That's the relay that I replaced. I'm going to put the old on back in. At least that one worked every once in a while. Even though the relay that I ordered is the one listed in the installation manual, it looks different than the one that was in there.

I responded to your post awhile ago, but not sure what happened to it. Anyway, I did replace the relay that you mentioned, no go. I put the original one back in ,no go. Now I've replaced the thermostat, no go. I'm at the point where I need to back off for a bit before I do something I'll regret. So frustated