Yes, every weapon can mount and has special mounting attacks while mounted (the gunlance for example stabs the monster and then does a full burst).
That said, not every weapon type can just jump and perform a mounting attack and you need to use the environment to get airborne in order to perform mount attacks.
Everyone can jump off ledges, use slopes, wallvines, climbing vines, and even other players (greatsword launching attack) to get up in the air for mounting attacks.
There are also armor skills and charms that can help with mounting (instead of landing 3 mounting attacks, you only need 1 for example). Check with the smithy on which armor piece has this skill
I haven't used it, but there is also a mantle that apparently really helps with mounting as well.
Personal anecdote: I main gunlance and almost always get the most mounts per hunt(unless there is an Insect glaive user in my group)