How can I find ISIN numbers for stock options?

Because an equity option can be constructed at essentially any price by two willing counterparties on an exchange, there are not enough ISINs to represent the entire (i.e. infinite) option chain for even a single stock on a single expiration date. As a result, ISINs are not generated for each individual possible options contract. Instead the ISIN is used only to refer to the "underlying" symbol, and a separate formula is used to refer to the specific option contract for that symbol:

16    - last two digits of expiration year
05    - expiration month
13    - expiration day
C/P   - call or put
00642 - dollars in strike price (00000-99999)
500   - decicents in strike price (001-999, but usually ending in 0 or 5)

So that code you pasted is not an ISIN but rather the standard US equity option naming scheme that you need to provide in addition to the ISIN when talking to your broker.

Note that ISINs and formulas for referring to option contracts in other countries can behave quite differently. Also, there are many countries and markets that don't need ISINs because the products in question only exist on a single exchange. In those cases the exchange is pretty much free to make up whatever ID scheme it wants.

P.S. Now I'm curious how option chains are identified for strike prices above $99,999. I looked up the only stock I can think of that trades above that price (BRK.A), but it doesn't seem to have an option chain (or at least Google doesn't show it) ...