If he never bet against his team, I don't even have an issue with him betting.
I'd vote for him to be inducted into the HoF immediately.
He never gambled on his on team, but he may have had inside info on other teams (injuries, team dissension, pending trades, tired opposing pitcher], or other info which would help him on his betting. Info regular bettors would not have access to.
Rose has admitted that he gambled on his team. He picked them to win every night. He never bet against them. At least that has never been admitted or proven.
Gambling is wrong and against the rules. IMO he has served his time. I do not think he should be allowed to coach again but he deserves to be in the HOF.