If the system install disc version is not the correct one for the iBook G4 build model,
odd effects may result. And if there is a version 10.4 grey label install DVD from a
MacBook, that may not work at all, even though early Intel macs shipped with 10.4
their installer was specific to that architecture.
Usually an iBook G4 setup from booted Install-restore DVD, does not ask for a
bluetooth mouse nor does it require the presence of one for the install to work.
(Mine certainly never asked for one; in fact no portable Apple I've had ever did.)
In the window as appears in your screenshot, can you click on the arrow in the screen
that may move to the right and expose more information on another window?
If you have an appropriate Bluetooth wireless mouse, you could attempt to use it.
However the built-in trackpad is USB and if there is a hardware issue, one would
usually try and use a regular USB Apple keyboard and wired mouse. I keep spares
on hand for use with portables and also to have backup or to troubleshoot issues.
As the time here is after 3AM I'm not able to offer much/any suggestions, & should
be going offline to attempt sleep; so I'm sorry that my reply isn't all that helpful...
Hopefully someone will be around and may offer a reply based on having seen
the screen while attempting to set up an older PowerPC based white iBook G4.
One that appears to also be asking for a wireless Mighty Mouse or similar.
Good luck in your effort to gain further progress in this situation... 😐