If a service member is suspected of a crime, At what point do they need to be read their Article 31 rights?

If you are not a MP/CID or in their chain of command. Then the answer is NO. If you did verify that they were, in fact, driving a stolen vehicle then you are required to immediately notify the MPs and report them.
The MPs will take a statement from you that you did see them and had knowledge of them driving a stolen vehicle.
Art 31 rights have a different "trigger" point than Miranda rights. The MPs will decide when to read them their Rights.
Personally that would be as soon as they sit down in front of me in the office. If I discover they are not at fault no harm no foul. If they were driving a stole car and charges need to be preferred. I can use everything they said to me after they signed the 3881

Just report it and let the Command decide. That decision will be made at a higher level. Report to the police. Let them make that call. Inform the command and they follow up with the Police. The brass will make that call. I would just standby and support as needed. If it has gotten to the point that a vehicle was stolen just report it due to the old adage "see something, say something". But to answer your question I wouldn't think to stop to read someone their article 31 rights while they were actively committing a crime would be feasible or logical. Just make the call and let LEO jump that hurdle.

Depends on the jurisdiction.... civilian courts don't need to read you art 31 since they would be charging you under local laws or title 18