Box outside my y axis in matplotlib/seaborn

Question

I"m trying to add a descriptive box outside my y axis on my heatmap in matplotlib/seaborn. I tried an additional subplot and hspan, but they weren't working for me. Help please!

import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns
import numpy as np

col1, col2 = np.random.rand(31), np.random.rand(31)

df = pd.DataFrame({'first': col1,
                   'second': col2}, index = range(70,101))

fig, ax = plt.subplots(1,figsize = (5,10))
sns.heatmap(data=df, annot=True, cmap='RdYlGn', cbar=False)
ax.invert_yaxis()
ax.tick_params('y', labelrotation=0)

Here is a picture of the box beside the y axis for reference.