Gate openers are often referred to as latches and you can get them at any major hardware supplier for as much money as you would like to pay. Some are not very flashy and others are very cheap.
Garage door openers do not get "wired." They are sold with a standard 3-prong, 120VAC plug that is about two-feet long and plugs into a 15A, 120VAC outlet -- next to the location where the opener is...