i wouldn't advise turning left cuz it could easily be assumed you made an attempt to go to second then they can tag you out if you don't get back to first. but turning right or staying straight is fine

I coach TTAB eec ball, last year it was just as you put it, but this year in the coaches meeting thy made it the old school way. I asked about it since I have inexperienced players, but they wanted to have it "no left turns". The head umpire said it was too easy to have a misunderstood situation, thus upset players. In this rec league, I liked it better the other way, the kids would turn left and the coaches could continue to teach them the correct way w/o them being called out. My experienced players, meh, but it's the "less than" players that seem to get the brunt of it.

FYI, in select/travel, I go with no left turns.

You can turn either way, the rule states as long as there is no intent to go to second on your turn.

I agree with Coach Moore. All the plays I've seen when the player overruns first, there might be a reason why he might go toward second - like an over throw or drop. If he makes a move toward second, then tag him out. If not, it doesn't matter which way he turns.

It's a good idea to teach the runners to pass the bag and look right after touching first for an overthrow and chance to advance. Just to be safe, teach to turn to the right if there is no need to make a move to second on that play.