According to fordparts.com, my 2008 has this mystery relay as well.
Looking in my Battery Junction Box and Smart Junction Box, there's no relay with markings 13350 or SF-631 (or -620, or -621).
Similarly, and as others have stated, the Ford 2008 Escape, Mariner Wiring Diagrams manual shows turn signals are controlled by FETs in the Smart Junction box. No relays used in the turn signal circuitry except for the tow package (and those are a different part number).
Personally, if this relay did exist, then there'd be some reference to a Ford P/N 8L8T-13350-AA. So far I can't find one.
While the 2001-2004 E's may have used this relay for the flasher, later models did not.
I think it's a simple error by Ford copied without question by the parts resellers. Then the LED flasher manufacturers use the same flawed info to cross-reference their products.
I know this doesn't answer the original question, but I don't think it possible to address the hyperflash issue without resistors (which present an equivalent to incandescent bulb load to the SJB logic) or reprogramming the SJB logic (if that's even possible).