As a deer stalker for over 25years , i must say it is refreshing to find someone who is quite willing to put in the extra effort for no personal gain .
Generally stalkers if there are any there have already assessed the state of the herd, the population and general sex ratio , after seeing a certain amount of damage where it occurs and the height of it , then an the amount and sex and species of deer can be generally agreed .
Alot of surveys can be done by deer droppings being counted
The main problems if the deer are Roe, then they have usually twins every year ,as do Muntjac so both species are successful in expanding and this expansion stops in-breeding but with Roe they can inter breed ( i have shot two roe with both female and male genitial ) . So a survey can help to stop this so can stalkers , also get in touch with the police reference road accidents in the area involving deer, the wildlife officer for the area should help you here .
The best way to survey them is to use with permission the high seats that the stalker uses, early in the morning and late evening i do not think you will gain any thing by staying overnight except a bad nights sleep.
If the species is Fallow then they mainly travel through the wood leaving a master buck and a few does so it would be difficult to assess .
As James suggested if there are alot of deer then stalkers are usually present and guard the area jealously and do not like other people assisting with there job. They also should keep records of all deer shot, where, when, sex, weight,species, and any problems like one antler etc this might help your interest.
If asked to control deer in an area i would normally survey an area for a few days first and submit my findings and reccomendations to the estate and agree a policy
all the best any other questions or points please get in touch
david s