Sorry that this is an older response to your post, but since we just "met" in the other thread, hope you don't mind me responding here.
I get this request quite a bit. I also have super high pitched squeaky/mouse hiccups, but don't get them when I cry. It's usually after I drink something carbonated or alcohol. I do have a client who will tip me to drink in free chat, and just sits and waits for me to do it. It's usually just one or two, but sometimes I get as many as ten. He always tips me after each one, which is sweet.
Wish I could do it on command. Would love to make a video of it. I've tried getting my phone out to take video, but they're usually over by the time I get to the record button.