As part of the concentration of artillery resources for 1st July and onwards, X/49, Y/49 and V/49 trench mortar batteries (TMBs) were attached to 32 Division with effect 14 Jun 1916. This HQ 32 Division order of19 Jun 1916 both shows where they were billeted and that their role was to help in the movement of ammunition
https://www.ancestry.co.uk/interactive/60779/43112_2373_0-00000?backurl=&ssrc=&backlabel=Return#?imageId=43112_2367_0-00532The order refers to an earlier one which is not in the record which may have dealt with the other halves of split batteries. It is clear from this and from other relevant records that none of the 32 Divisional artillery’s firing orders, firing programmes or ammunition plans have any mention of the heavy trench mortars. Snippets elsewhere confirm the use of the manpower of some of the TMBs during the preliminary bombardment and the offensive actions from 1 July 1916 on different tasks.
For context, the attack of 37 Division on Pozieres, with the East Lancs, was from the south. 32 Division was coming from due west of Pozieres. The 32 Div artillery massed for the offensive was deployed (reference here is to the map in the earlier post) in squares W 18, W 11, W 12, Q 33, W 12, W 5, W 3 (11 batteries in total) and in W12, W9, W 17 (4 batteries). Heavy artillery and a group of French artillery were also employed. The situation was similar in 29 Division (courtesy of a forum member elsewhere) where the heavy TMBs were used in the preliminary bombardment but not once the offensive had started.
Thus the best one can say about grandfather’s whereabouts is that he was humping ammo or helping with digging work somewhere around Aveluy, perhaps billeted with the half in the cellars of the Café de la Mairie in Rue de l’Eglise (the Mairie is now a school, no sign of the café – Google Earth).
So while I can’t improve much on your first thought that grandfather was in the same area as the East Lancs, hopefully the above zeroes in just a bit closer on his whereabouts in those dark days. You may be able to include Aveluy in your travels.
MaxD