If you enter RANDOM with the same number (be it zero or otherwise) it will always produce the same repeatable sequence.

If you had your five projects, all identical, all powered up on the same day for the first time, they will all produce the same result. To ensure that didn't happen, ensure the contents of EEPROM location zero differs for each project (see DATA statement), or power each PIC on/off a different number of times (since location zero alters each time) and the projects will then all be following a different switching pattern.

Yes you could add a Random result instead of 23 as you say, but it won't make it any more random. This is because we are going to cycle through 256 possible Random start sequences anyway (as EEPROM location zero is a BYTE variable), and therefore a BYTE only has 256 possble states with which we can start seeding.