To find it:
1. Locate the fuse box: This is usually under the dash, on the driver's side.
2. Look around the fuse box area: The flasher relay is often a small, square or rectangular component plugged into the fuse box or mounted very near it. It might be attached with a small clip or simply plugged in.
3. Consult your owner's manual: Your owner's manual should have a diagram of the fuse box and relay locations. This is the most reliable way to pinpoint it.
4. Check online resources: A search for "2003 Chevy S10 turn signal flasher location" coupled with images might reveal photos showing its location in other S10s.
Important Note: Some S10s might have the flasher integrated into a larger module rather than being a separate relay. If you can't find a standalone relay, that's a possibility.