matplotlib: hide subplot and fill space with other subplots

I've got a figure that contains three subplots which are arranged vertically. Once I click into the figure, I want the second subplot ax2 to be hidden and the other plots to fill the space. A second click into the figure should restore the original plot and layout.

Hiding the subplot ax2 isn't a problem, but how can I rearrange the positions of the other subplots?

I've tried creating a new GridSpec, using the set_position and set_subplotspec methods, but nothing worked out. I'm sure I'm missing something here, any help would be appreciated.

This is my code:

import matplotlib.pyplot as plt
from matplotlib import gridspec

fig = plt.figure()

gs = gridspec.GridSpec(3, 1, height_ratios=[5, 2, 1])
ax1 = fig.add_subplot(gs[0])
ax2 = fig.add_subplot(gs[1], sharex=ax1)
ax3 = fig.add_subplot(gs[2], sharex=ax2)

visible = True

def toggle_ax2(event):
    global visible
    visible = not visible
    ax2.set_visible(visible)
    plt.draw()

fig.canvas.mpl_connect('button_press_event', toggle_ax2)
plt.show()