The button on the back is for holding the bobbin (according to Thomson Tackle Tolls catalog number 17) between the two fore fingers. One of the advantages of using this bobbin was the ability to retract thread (that was pulled out to wax) by dragging the bobbin, spool side down, across the table.
I have been searching the internet for more information on the Thompson company. FYI he made a bobbin that would take two different colors of thread. These were sold to the Gentlemen who tied salmon flies. There was a spring between the two spools that added tension. Seems that these were sold to the European market. Looks the same as what your picture shows only with 2 spools and spring apparatus.
Yes LH the problem is D.H. Thompsoi is the patent holders daughter. Herbert L. Thompson is the patent holder and holds over 100 patents. More info has come to light. Seems that the family was a little excentric. The address given is for the family residence not the company's manufacturing location.
Possibly they ran there office out of there home. If you do a google map (street veiw) it is in the middle of a residential neighborhood. That is one reason that things are hard to track down. The company has changed its name at least three times. Then it went out of business and records got lost to time. People that worked for the company left or died off and history was lost.