The Only Temple that is Open during Eclipses is Sri Kalahastheeswara Swamy Temple,AP.

Mythology claims that the idol of Lord Shiva present at this Sri Kalahasti(Vayu linga) has all the 27 Nakshatras (stars) & 9 Rashis and is believed to control the entire solar system.(1/4) https://twitter.com/Fasakkkkkk/status/1161166639468933120

This temple is called as Rahu Kethu kshethram.
Both Rahu and Kethu were with Swamy & Ammavaru(Parvathi). According to mythology,a 5 headed serpent called Kethu adorns the head of Lord Shiva whereas a single headed serpent called Rahu in the form of an ornament of Ammavaru.
(2/4)

In any Temple during Eclipse,
'Sin Increases,Virtue Decreases' in the presence of God.

This is the Reason why temples are closed during this period
But in Sri Kalahasti temple,both Rahu and Kethu are worshiped & there will not be any evil effects on the temple.
(3/4)

As this Temple has Rahu & Ketu are associated with Dieties, the ill effects of eclipse not to be felt in this temple.
This temple helps in Correcting Horoscopic Defects.

This temple is significant because it is one of "Panchabootha Stalam" Temples.(4/4)