Air carrier Captain reported departing the gate without signing the Hazmat declaration due to a maintenance distraction in addition to other time critical departure issues.

Narrative

F/A (Flight Attendant) reported inoperative reading light en route to ZZZ. ACARS message sent en route for MX assistance upon arrival. Company Mechanic evaluated and determined problem was not light but light switch and communicated need for deferral. Mechanic departed with logbook and subsequently returned with logbook indicating deferral and placed white sticker in appropriate place. Dispatch sent ACARS message to have Captain call for obligatory conference call with MX Control regarding deferral of this inconsequential writeup. During this effort; ZZZ Supervisor verbally asked if we were aware HAZMAT in the form or radioactive pharmaceuticals were being loaded. With F/O (First Officer) attentive to this conversation; I (Captain) confirmed with Supervisor that a HAZMAT declaration would be brought for my signature.As both the F/O and I were busy preparing the flight deck for the next leg; and simultaneously attempting to eat our dinners; I called Dispatch for the required conference call. While the Dispatcher was aware of the MEL number (25-XX-XX); his system did not reflect the nature of the deferral. This MEL covers a myriad of non-essential cabin items. As a result; I had to read the actual discrepancy to the Dispatcher for him to be informed about the issue. The conference call (as usual) was neither informative nor helpful. It was purely a requirement that fulfilled (in this case) no need.After the conference call; the Dispatcher; upon my request; patched in a Chief Pilot on Call to discuss the need for relief of this requirement and how it only creates an additive condition with no benefit to the Flight Crew (only an additional administrative requirement). Upon completion of this discussion; the takeoff data came through ACARS; and we proceeded to complete checklists and review performance data. Takeoff and climb out were uneventful; and en route Dispatch sent an ACARS indicating I had failed to sign the required HAZMAT declaration.