Signal lights and horn not working properly

Hello. I have a couple of questions here. One, has any custom type of work been done to this truck? Has it been "upgraded" to LED lighting or anything like that? If so, that will cause all sorts of funny flashing issues until the right flasher relay is purchased and installed, and sometimes other wiring work needs to be done, depending on the kit. Doing this type of work could explain the issues you're having. Frankly, the easiest way to fix it would be to go back to stock and start over.

But, if no custom upgrades have been done, then we're probably looking at a bad switch or flasher module. You say you purchased it, but have you installed it yet? Either way, let's make sure you got the right one. Because there are a few possibilities depending on various options and such. So, do you have a link to the one you bought, or a picture showing the part number so I can look it up?

If this checks out, then we need to look at scanning for potential trouble codes from the Body Control Module. You'll need a decent OBD2 Scanner that can read U codes. The OBD2 port is on the driver's side, under the dashboard, near the parking brake pedal. Just plug the scanner in, turn the key on, and follow the prompts to see what trouble codes (if any) come up.

Here's our guide: https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Regardless of if your check engine light is on right now, there could be Body Control Module codes stored, so go ahead and get it scanned. If you don't have a scanner, your local auto parts shop does.

Let me know what you come up with.

Hello again. That 44810 flasher is an older model flasher. The newer GMs (roughly 98 and up) take a flasher module. Here's the one I have in my 2000 Blazer

(https://www.amazon.com/CEC-Industries-EF29-Flasher/dp/B0031GR7C4/ref=sr_1_4?dchild=1&keywords=2003+s10+flasher&qid=1632968887&replacementKeywords=flasher&sr=8-4&vehicle=2003-47-488&vehicleName=2003+Chevrolet+S10)

It's apparently compatible with your 2003 S10 as well, although I'd pull the flasher module and confirm that you have the 4-pin flasher and not a 3-pin flasher module. Note, this is a heavy-duty flasher, tailored towards vehicles that do a lot of towing. I use my Blazer on a mail route, with the hazards running 5 or more hours daily. I've had this flasher in for 3 years and haven't replaced it yet. The standard duty ones generally lasted me about a year and would just give out with no warning, and someone would nearly rear end my truck because with the hazard switch on, and that module fried, there are no brake lights.

Anyways, turn on your flashers. Open your glove box. There's a tab at the top of it, I think on the left side. Push it in to release the glove box door to swing all the way down. Now follow the flash sound to the clicking box. Unclip it and replace it. See what happens.

Honestly, I'm thinking it's a body control module issue. Looking at the diagrams, I see no connection between the clock spring and the turn signals. The only connection between the horn and turn signals that I see is the BCM. If you'll look at these images, you'll see that it's all tied in to the BCM. I'll do some more digging in a bit to figure out a diagnostic procedure. But if you have a donor truck that you can borrow one from that would make things easier. I once bought a BCM off of eBay for $25.00 for a 1999 Buick when I didn't have a reliable test method at my disposal. The car wouldn't crank at all. BCM solved the issue, as it was related to the security function of the BCM.