if a cef lets you reinvest dividends at market price, it is easy to do so. but, some seem to argue, you would do better taking dividend in cash and picking a better time to buy shares in the cef. they argue market price is higher at time of dividend reinvestment than it is normally or especially if buy when market price is low and/or when it is at a bigger discount to nav than normal.
language is complicated re price paid when do dividend reinvestment.
i seem to remember long ago there were dividend reinvestment plans for stocks and for cefs where you reinvested at a % less than market price. that no longer seems prevalent or even available.