How can you determine how long the MAC for GCM must be?
In Recommendation for Block Cipher Modes of Operation: Galois/Counter Mode (GCM) and GMAC Appendix C, Table 1 &amp; 2 NIST gives the recommended maximum number of invocations of the decrypt function of GCM for different message lengths using a MAC of 4 and 8 Byte.

My message length of 7 Byte cipher text + 0 Byte additional authenticated data (AAD)  enables me to decrypt $2^{22}$ and $2^{32}$ messages respectively, before having to change the symmetric key.

Since in my application I want to send $2^{32}$ messages before I'll have to change the key, I'll have to use 8 Bytes.