What do solo pilots do between reporting points on longer flights?
The short answer is that you keep checking everything in the aircraft is doing what it should. For light piston GA operations, one common acronym for en route checks is FREDA. Here are some things that could be included (pilots often use their own checklists for things like this):


Fuel. How much have I burned? Is my navigation log up to date? Have I burned the amount I expected? How much longer can I fly for before I have to land? Which airports are within my current range ring? Is it time to switch tanks? Is the aircraft still within weight and balance limits? Is the airport where I planned to refuel still the right place to go?
Radios. Do I have all my radios set to correct and useful frequencies? How am I going to identify my next waypoint? Do I need to tune and identify a new VOR? Have things been suspiciously silent for a while? Should I file a PIREP? Do I need to tell ATC I need a deviation for weather? What's the latest weather information from ADS-B or another source? Can I guess which frequency ATC is going to hand me off to next? Did ATC ask me to report at a certain time or place?
Engine. Are all temperatures, pressures, gauges etc. showing the values I expect? Have I leaned the mixture properly? Are the exhaust gas temperatures correct? Is manifold pressure correct for this altitude? Has anything changed unexpectedly since the last time I checked them? If the engine dies right now, where am I going to land?
DI to compass. Reset the directional indicator to match the wet compass, to avoid gyroscopic precession errors.
Altitude. Is this altitude correct for my current heading? Is this the altitude I was assigned? If I lose comms now, what altitude should I fly at? Do I know what terrain is below me? What's ADS-B showing me right now? Any potential traffic conflicts? If I encounter icing here, will I descend, climb, or turn around? Is the autopilot correctly configured? Have I entered the current altimeter setting in all the instruments?


After you've worked through all that, it's usually time to go back to the beginning and start again :-)

Of course, there are plenty of other things that pilots are likely to be doing, like having drinks or snacks, taking pictures, admiring the view, listening to music, trying to find their spare headset batteries at the bottom of their flight bag, and so on.

But an IFR flight - or any flight - is never just sitting back between waypoints and waiting for ATC to call. The point of the constant checks is to detect any problems as soon as possible. For example, if you notice the oil pressure dropping gradually, you can take action while you still have engine power; if the first you know about it is that the engine suddenly stops then you have a big problem. Not only have you lost engine power, you're also not mentally 'primed' to deal with the situation and that could turn a tricky situation into a dangerous one.