How can I troubleshoot an Epson Perfection 1260 scanner that won't play nice with Mavericks?
The red light may mean that the scanner has detected an internal error, so start at that end.  First, try the scanner on another system if possible. If it works on another system, then the issue could be the USB connection or the software.

It is not unheard of (though rare) to have a bad USB cable, so if you have a spare, swap it for the current one and see if that helps.

There were sporadic disconnects in the early versions of Mavericks, so a system update may have solved your problem.  If not, start troubleshooting by making sure your software is up to date, then remove all other peripherals from your system and connect the scanner directly to your Mac ( no hubs ).  Try each USB port in turn, as there are differences in their internal connections.

I doubt that it would make any difference, but you can download and try a copy of vuescan, (hamrick.com) which uses a different driver.