Accessible MVs are a different ballgame than normal ones.
It's normal during busy times (rain, park open, park close, events) and possible at all times. Normally I'd say I can get one within half an hour if I'm not during any of the above BUT there are only a few at most and depending on if they are in the shop they can have as little as 1 accessible MV running. This is why it is advised to leave enough time to get to your destination via alternate transport (like Disney transport) in case you cannot secure a MV. Personally if I have not secured a specific van (meaning I have a number and the van showing on the app) within 20-30 mins I bail and go with the alternate transport option.