The timestamp is used for allowing the server to optimize their storage of nonces. Basically, consider the read nonce to be the combination of the timestamp and random string. But by having a separate timestamp component, the server can implement a time-based restriction using a short window (say, 15 minutes) and limit the amount of storage it needs. Without timestamps, the server will need infinite storage to keep every nonce ever used.
Let’s say you decide to allow up to 15 minutes time difference between your clock and the client’s and are keeping track of the nonce values in a database table. The unique key for the table is going to be a combination of ‘client identifier’, ‘access token’, ‘nonce’, and ‘timestamp’. When a new request comes in, check that the timestamp is within 15 minutes of your clock then lookup that combination in your table. If found, reject the call, otherwise add that to your table and return the requested resource. Every time you add a new nonce to the table, delete any record for that ‘client identifier’ and ‘access token’ combination with timestamp older than 15 minutes.