When is the best time to activate Glyph of Fortification on T3 Buildings?

I was in a game where we got team wiped on the last team fight, and the enemy team was trying to take down mid Tier 3 Towers and Barracks. I proceeded to activate glyphs when the tower was about 1/3 health. Then one of my teammates said that it was the wrong timing and it should be used when they start trying to take the barracks. We later on won the game but that made me wonder, was my teammate right?

The Tower Argument

The way I see it, the tower gets 100% concentrated attacks from both enemy creeps and heroes and is the last line of defense before the barracks become vulnerable. This means that the glyphs would soak up more concentrated damage in that 5 seconds than the damage on barracks (which may potentially be split on the two barracks if the enemy isn't smart about it). The tower basically has twice the armor than barracks (more than 2x for ranged) and slightly more health, so to me, the better strategy is to preserve the best defense and block concentrated damage.

The Barracks Argument

On the other hand, activating glyphs on the barracks also seems to makes sense because it gives 5 seconds of blocked damage on weaker buildings where it otherwise would have melted in 3 seconds or less. Also the hope that they will attack separate buildings after the tower is gone is not a very good argument. So, which is better?

More Situational Context:

• 3 of us were about 15 seconds or less from respawning, so using glyphs was semi-viable
• This would be the first T3 tower/rax take down attempt on our base (other lanes were still up)
• Enemy team was 5 man during the take down