True "random" is tricky, as the Tricaster macro engine does not have random generator (usually productions tend to avoid "random" things)
But depending on the device you have I can suggest the following:
Create a manual macro of randomly punching in cameras between INPUT1-5. After the recording is done, open up for editing, and between the cameracuts on PGM, set the delay everywhere 10-15seconds (you can either calculate it in frame, or say 10000m as a delay, which is going to be 10000 ms = 10 sec).
Press Ok, close the macro, let's make sure it loops, and it's going to loop your previously created macro infinitely.
If you want true random, follow tveng's suggestion.
I want to add few things:
1. Our REST API uses digest access authentication, so you have to handle that in your program code (or remove the LivePanel password from the system)
2. If you want to do it more elegantly first you select a http://{IP Address of TriCaster}/v1/shortcut?name=main_b_row_named_input&value=INPUT{randomlygeneratednumber} and then do a "take" please http://{IP Address of TriCaster}/v1/shortcut?name=main_background_take
In this case you are selecting a cam on PVW, and then it does a take. Introduce a 1-2 frames of delay between the two commands.