Personally I think if there was some research done on every manager in English football from the last 20 years, and manager animation on the touchline was plotted against teams performances on the pitch, there'd be no correlation between the 2.
For me a manager's work is done on the training ground, in their office and in the dressing room. Once players take to the pitch, for me all a manager is doing is watching for things to mention at half-time, full time, and maybe during the odd drinks break if there's an injury. And for which subs to make.
In terms of shouting things from the touchline, I really don't think players can hear, or that managers should even be trying to change things at that point, after coming up with a gameplan all week.
Be it Dalglish stood there calmly in his big brown coat, Souness and Hughes mid-way on touchline animation, Allardyce sat in the stand first half, Mowbray expressionless, or JDT with his hands in his pockets mostly expressionless, doesn't affect the score in the slightest IMO. Maybe in amateur football it helps players, but for professionals a manager hopping about is just another fan to go with the other 15,000 they zone out.