How about suggesting your manager that, if no overtime taken into consideration, then a bigger hourly rate should be taken into account. Like a measure to balance somehow your real work effort with the official timesheet.

Also, something like "the consultant would have to be available to perform tasks when required, no less than X hours/week" would balance the situation, just by raising a bit (or more) the number of your working hours.

Anyhow, it seems that a new agreement should be reached ... and you should claim the balancing factor. For example, if you work like 30 hours/week and get paid for 28, I'd say you could live with that, but if get paid for 20, that might be a problem. You should prepare this kind of report, BEFORE talking to your manager.