A good place to start learning about option market making using quantitative techniques is Euan Sinclair's Option Trading (chapter 10 is devoted to market making techniques). He also gives a decent introduction to a more sophisticated quantitative market making technique which he calls information-based market making. Specifically, he explains how to apply Kalman filtering to optimally incorporate new information into an estimate of value.
Sinclair's Volatility Trading is also a good reference for options, but more geared towards aggressive strategies that attempt to predict where the market is headed.
As for your actual question regarding market making in illiquid markets, I believe your best bet is to learn all the Greeks well and try to create tools to manage them in real time. Your question suggests that you would like to hedge your individual equity options with index options. Index options are generally a very poor hedge for the options on the constituents of the index. Rather, most market makers dynamically hedge by trading the underlying and by trading other options contracts on the same underlying (different strikes/maturities) that may be more liquid. Remember that, at least in theory, an option can be perfectly hedged by dynamically trading the underlying. In practice, due to the risk of jumps in the underlying and to hedge higher order Greeks, market makers attempt to hedge using other options (in the same underlying) first, and then hedge the residual exposure by trading in the underlying.
A good way to start learning, as Sinclair writes, is mimicry:
If a trader has no clue where to quote a market, a good trick is to identify a competent trader and post the same prices as him. The identification of the “competent” trader is not actually crucial either. This trick works purely because it keeps the trader on the general market and hence collecting the bid-ask spread. And as we saw in the Chapter
on volatility trading, even hedging these trades at the current implied volatility gives as good a result as anything else. This method is good for generating revenue, however it is poor for inventory management and traders using it will find themselves with problems
as they approach expiration.