12835/36 has two dedicated rakes for sure.. I was a frequent traveller of this train.. And yes i have seen the empty rake of 12811/12 several times at hte yard..
The rakes which comes from anvt as 12818/74 can never run as 12835 due to their timings as 12835 departs hte at 18:25 and those rakes from anvt never reaches hte before 18.25.. So if there is any rake sharing then it may be between jsj and hte-ltt sf but impossible with 12835/36..