Armadillo peeking animation plays at normal speed at high tick rates

When in a world with a very high tick rate - e.g. 5000 - most mobs have quick animations.

Armadillos are similar - their rolling/unrolling animation happens quickly at high tick rates.

But the peeking animation plays at normal speed, and therefore causing it to stop mid-animation to peek again.

How to reproduce:
Set the tick rate to a very high number, e.g. 5000 (/tick rate 5000).
Summon an armadillo.
Place a shaded undead mob near the armadillo.

Expected Result:
Like its rolling and unrolling animation, the armadillo should peek out at a high speed.

Observed Result:
Yet, peeking still happens at the normal speed, causing the armadillo to peek again before one peek finishes.