Specifying Time as a Random Effect?

I have a simple question regarding using time as a random effect.

Briefly, I am modelling population-level changes in the movement rates of 68 woodland caribou using generalized additive mixed models that have been specified using the function gamm4 from the R package gamm4. I have calculated the daily movement rate for each animal over a two year period (i.e., km/day per animal). Since repeated rates were calculated for each caribou, I am including the animal id (AID) as a random intercept in my GAMM. An example of my model is shown below:

model1<-gamm4(daily.rate~s(yrday, bs="cc", k=-1), random=~(1|AID), data=caribou)


where daily rate is actually the log of the raw daily rate, yrday is the day of the year (1-365) and AID is individual animal id (001....068).

However, I also want to account for potential annual variation in movement rates. As I understand it, year and animal id are crossed random effects which means that if I were to include Year (1 or 2) as a random effect, I would specify the model as follows:

    model2<-gamm4(daily.rate~s(yrday, bs="cc", k=-1), random=~(1|AID)+(1|Year), data=caribou)


BUT, I also understand that random effects should have at least 5-6 levels, otherwise it's difficult to measure among-level variance. Since I only have 2 levels to the variable Year (1 and 2), I don't think I should be including it as a random effect. My question is this: should I include it as a fixed effect? Any advice would be much appreciated!