Does blink work inside a forcecage?

Assume Hackslash the dwarven bard is currently fighting to the death against Glarcyon the gnome wizard. Hackslash successfully trapped both of them inside a forcecage, and Glarcyon already failed all charisma saves (woe to you, -2 dump stat) to try and exit the forcecage. His only defensive spell left is blink. None of his offensive options can finish Hack in one turn.

Unless he can shift to the ethereal, he will pay the ultimate price for making fun of the College of Valor this very round.

But if he can get to the ethereal plane, he can use his McGuffin of Ethereal Spell Slot and HP Restoration to win the battle.

But can he blink inside a forcecage?