Lots of part 135 operators don't use dispatchers. And for the ones that do, there is no regulatory requirement for them to be licensed, if that is what you are looking for.
I can tell you that Ameriflight does have dispatchers for all of our flights. And while they aren't required to be licensed, many of them are. And they perform similar to 121 dispatchers as regards tracking flights, verifying destination and alternate weather, etc.
I don't know what bases are actually hiring right now, but I know we do hire on a frequent basis. Check on the company web site (
Ameriflight | Above & Beyond) and check the employment page regularly to catch the hiring announcements.