The final device is only capable of 20 watts max. But it is unwise to run it that high. Meters aren't that accurate, except for the Bird and only a select few others.
On AM mode, if the Bird tech can tell you that you are dead keying 4 watts with a peak power of 16 watts - that would be ideal. A 4:1 ratio of dead key to PEP (peak envelope power) with 100% modulation is correct.
On SSB, it will probably swing to 18 watts if he adjusted the ALC and the waveform looks is unclipped/undistorted on an oscilloscope. Most techs know this, or they don't stay in business too long . . .