I have tested some different switches and IOS version, this is my result
Switchtype IOS 1.3.6.1.4.1.9.9.220.1.8.6.1.1 1.0.8802.1.1.1.1.2.1.1.6 1.0.8802.1.1.1.1.2.1.1.5 1.3.6.1.4.1.9.9.220.1.1.1.2
Catalyst-2960-48-TCL 122-52.SE.bin OK OK Not Ok OK
WS-C2960-48TT-L 122-52.SE.bin OK OK Not Ok OK
WS-C3750-48PS-S 122-52.SE.bin OK Ok Not Ok OK
WS-C2960S-48LPS-L 150-2.SE2.bin OK Not Ok Not Ok OK
C2960S-24TS-S 150-2.SE2.bin OK Not Ok Not Ok OK
WS-C2960S-48TS-L 150-2.SE2.bin OK Not Ok Not Ok OK
WS-C2960G-48TC-L 150-2.SE5.bin Not Ok Not Ok Not Ok OK
Not easy to read but the best OID (for me) is 1.3.6.1.4.1.9.9.220.1.1.1.2
It gives three results, 1,3,4 Four is tells me that we use 802.1x, others false
Next opportunity is to find ports that is "Sticky"