Are there any mechanisms in the TLS 1.2 protocol (not implementation) against timing attacks? For example, that the handshake response time should be padded to X milliseconds? Or should I implement such mechanisms manually ?
Yes. See the RFC for TLS 1.2 (RFC5246) and note the MUST.
Implementation note: Canvel et al. [CBCTIME] have demonstrated a timing attack on CBC padding based on the time required to compute the MAC. In order to defend against this attack, implementations MUST ensure that record processing time is essentially the same whether or not the padding is correct. In general, the best way to do this is to compute the MAC even if the padding is incorrect, and only then reject the packet. For instance, if the pad appears to be incorrect, the implementation might assume a zero-length pad and then compute the MAC. This leaves a small timing channel, since MAC performance depends to some extent on the size of the data fragment, but it is not believed to be large enough to be exploitable, due to the large block size of existing MACs and the small size of the timing signal.