I watched a video of steam engine SP 4449 as it made its way from Oregon to Los Angeles’ Union Station for the station’s 50th anniversary celebration (1989).
One segment was photographed in the cab as the engineer started a speed run. He appeared to be working two throttles, one horizontal with his right hand slightly below chest level, the other vertical with his left hand at head level and hinged from the cab’s roof.
The two controls you saw are analogous to the accelerator and gear shift on your car. The one on the right is the reverser which controls the admition of steam to the cylinders. All the way forward maximumsteam for pulling power, as it’s moved toward the center the duration of admision is reduced for sustained high speed. the throttle hung from above and operated by the left hand controls the amount of steam leavung the boiler and going to the valve (which is controlled by the reverser). Basically the throttle controls the volume of steam and the reverser controls the length of time it’s admitted to the cylinders (and, of course, the direction of travel)
The engineer would work the right-hand throttle, then pull on the left-hand control, then back to the right-hand, then the left, until he attained the speed he wanted. Each time he worked the left-hand control, he seemed to pull it as far as it would go. It took effort to pull back that control, and he appeared to pull it back the maximum amount each time, getting a little farther with every effort. Lots of instruments, gauges and indicators inside that cab.