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It sounds like you are either having a communication bus issue or the instrument cluster itself is failing.
All of the modules on the vehicle communicate with each other over a communication bus network. If the instrument cluster loses communication with any module it will light the appropriate warning light. If it is losing communication with the ABS module, trans and engine controllers then it will cause exactly what you are having.
A bus problem could be an internal failure in a module that is shorting the network to a high or low voltage or it could be a wiring issue.
It may also be the cluster itself that is the only thing losing communication because of an internal failure.
The first thing that will need to be done is use an appropriate scan tool to see what fault codes are stored in every module and this will tell whether the problem is widespread or just the cluster not communicating. If all modules have fault codes for lack of communication with each other then the bus is going down but if there are only codes for lack of communication with the cluster then it is most likely the issue.