Any on-demand pseudonym acquisition strategy is problematic should the connectivity to the credential management infrastructure be intermittent. If a vehicle runs out of pseudonyms with no connectivity to refill its pseudonym pool, one solution is the on-the-fly generation of pseudonyms, e.g., leveraging anonymous authentication. However, such a vehicle would stand out in the crowd: one can simply distinguish pseudonyms, thus signed messages, based on the pseudonym issuer signature, link them and track the vehicle. To address this challenge, we propose a randomized hybrid scheme, RHyTHM, to enable vehicles to remain operational when disconnected without compromising privacy: vehicles with valid pseudonyms help others to enhance their privacy by randomly joining them in using on-the-fly self-certified pseudonyms along with aligned lifetimes. This way, the privacy of disconnected users is enhanced with a reasonable computational overhead.