So yes, monitor those VITAL instruments.
Mind you, some people can go overboard about monitoring. During take off from Canberra circa 1964 in a RAAF Convair 440 Metropolitan, and a few seconds after the landing gear had been selected up, there was a crescendo of noise from the port side with RPM needles indicating indicating an over-speeding propeller. There was no time to go through the standard identification routine so I feathered the left prop.. At this point the co-pilot had no idea what was happening and there was no time to discuss things.
It took less than six seconds for the prop to go from 2400 RPM to 3200 RPM before a stand pipe in the oil tank saved the day and enabled the prop to feather. Inspection through the port side cabin windows revealed oil covering the left engine cowls as well as the landing gear and over the tail plane. Made a circuit and did an asymmetric landing. Due for the potential for fire with hot brakes on the left wheels, we used no brakes on that side. Reverse thrust was used on the right engine and there was no problem with the landing run.
Later investigation revealed the main oil line from the engine to the oil cooler had split asunder, dumping approximately 35 US gallons of engine oil oil everywhere including on the runway during the latter part of the take off run. There were no untoward indications until the prop ran away.
In the Convair 440, the oil tank contents gauges are on the lower section of the instrument panel in front of the captain's position and hidden from view behind his control column.
It was not possible to view these gauges unless you leaned well over and looked down over the rather bulky control column. The wide cockpit layout on the Convair meant the co-pilot had almost no view of the oil contents gauges which were hidden from his view by the throttle quadrant and the captain's hands over the throttles.
Despite the successful outcome, the captain (Cent) was criticised by his Commanding Officer for not monitoring the two out of sight oil contents gauges during the take off roll. The CO claimed the beginning of the loss of oil contents should have been picked up during the 35 seconds of take off roll and a rejected take off undertaken.
Of course his claim was rubbish as the last instruments one would ever monitor during a take off roll are out of immediate sight oil contents gauges. Monitoring of flight paths and various appropriate gauges should be a common sense task by reasonably competent crew members. Pilots should not be required to have special prescriptive training courses just for these simple tasks