Republicans do our precinct conventions after the polls close at 7. Luckily we ran through a mock convention at our meetup so those new Precint chairs know what is going to go down.
Yes, Republicans in Texas DO have a convention. It is usually at the voting place and I believe can start between 7 and 9 depending on your county. Most of the conventions begin at 7, so get there on or before time in case of a hasty start.
In Harris county we got information from the GOP HQ that the convention cannot begin BEFORE 7:30 or the last person has voted, whichever is later. Make sure that you know the rules and follow them or else you risk having your whole convention thrown out.