The ‘cardiac chronotropic response’ on swallowing is where there is an abrupt initial rise in heart rate on swallowing, slowed rise in heart rate, and then recovery. he acceleration is due to inhibition of vagal activity. ‘Deglutination tachycardia’ is the average resting heart rate beforehand compared with peak during swallowing.
In normies, ‘the contribution of each swallow is lower than that of the previous one’ and  the parasympathetic compensation actually causes HR to drop after. The mechanism of swallowing is designed to be completed quickly to allow the resumption of breathing. 
The ranges for heart rate rise found in the attached study were:
supine position (13.1 +/- 5.6 bpm)
standing position (8.5 +/- 3.8 bpm).
Thus in the normal population 95% of people’s HR raised:
laying flat 2-24bpm
Standing 1- 16bpm
In the study, tests were performed in the morning (as mine was), after 10 mins rest in supine position (from resting), each patient completed a single swallow, three swallows, and five swallows one at a time, and then 7-10 water swallows through a tube (like i did using a straw). This is shown in the attached image, 1 is deglutination tachycardia, 2 is the addition of each bpm for 2 heart beats, across 1,3,5 swallows.

This video documents a rise of 68-92 bpm, laying reclined. The following day sitting knees up in a crouch position, resting 59 went up to 94bpm, a raise of 36bpm). Once PEM improved, EG able to move more under 100bpm, the repeat test of 7 swallows of water elevated heart rate 20bpm only (Resting 63- peak 83- dropped back to 61). This return to bradycardia is noted as part of normal parasympethic compensation. 

In PEM for patients the sympathetic dominance can cause high heart rates and breathlessness when eating or drinking. Difficulties swallowing can also be an issue due to swollen glands, sinus congestion, muscle weakness, stress etc.

The parasympathetic nervous system slows heart rate through the action of the vagus nerve. The response relies on the vagus nerve, which may be lacking tone, or inflamed? in ME/CFS/fibro. Thus in PEM there is sympathetic dominance, the HR isn’t slowed by the parasympathetic response, the parsympathetic response may not occur and the heart rate may continue to elevate beyond the third swallow. This may likely be inflammation, as if it was just a lack of tone it would presumably be constant across time, not just in crashes. This seems to be readily documentable evidence of vagus nerve problems, specific to PEM.