There's another tour sign on Bridgewater Road west of SR 513, but I don't see any east of SR 513.
one herePerhaps this should be a gap, since half of our route was never the National Road. Or take it on I-70 like https://gis3.dot.state.oh.us/ScenicByways/HNR.html shows,
I-70 would be a mistake, per the sign above. The PDF guide has the route off I-70, but with a break where it leaves the old alignment. Sadly there's no Streetview where the gap would be, so we can't check the bodge I did to avoid a gap (a touring route shouldn't have to only stick to the old route and then disappear - it should be a followable route - cf the signed twists crossing I-70 further west at Old Washington).
but there doesn't seem to be any signage to the east to and along SR 800 either.
There's
this, which says OH800 is a byway (that signage was considered an error and abolished in 2022 according to
AARW - however I can't check the source as Ohio DOT, like Iowa DOT, get around the EU's stupid cookie law that our stupid government haven't repealed by not allowing European access rather than spending a bit more money to have the stupid checkbox for European visitors) - ie it's a signo for the National Highway, using the generic instead of the specific.
Annoyingly the entirety of the Ohio River Scenic Byway in Ohio uses these signs, rather than the route specific one. Then again, Indiana uses the ORSB or LCTrl, or both, depending on what mood they are in and that's more complicated to deal with than the no build of 'it is not signed properly'!