The following MWE

import matplotlib

matplotlib.use('TkAgg')
import matplotlib.pyplot as plt

# Use latex
import os
os.environ["PATH"] += os.pathsep + '/usr/local/texlive/2024/bin/x86_64-linux'

if __name__ == '__main__':
    plt.rcParams.update({
    "text.usetex": True,
    "font.family": "serif",
    "font.serif": "Computer Modern Roman",
    })

    test_data = 10
    test_data_2 = 24

    # Create plot and axis
    fig, ax = plt.subplots()

    # Plot
    ax.plot([i for i in range(test_data)], [i for i in range(test_data)], label="Test")
    ax.tick_params(bottom=False)

    # Define x axis
    x_axis = ['30', '40', '50'] * (test_data_2 // 3)
    ax.set_xticks(range(len(x_axis)), labels=(x_axis))

    # Add second x axis
    sec2 = ax.secondary_xaxis(location=0)
    sec2.set_xticks([5.5 + 12 * i for i in range(test_data_2 // 12)],
                    labels=[f'nn{5 + i * 5}' for i in range(test_data_2 // 12)])
    sec2.tick_params('x', length=0)

    plt.show()

Results in the following plot

I would now like to be able to precisely move the secondary x axis up a bit (instead of using inprecise ‘n’). How would this be possible or should I maybe use a whole different approach for getting a secondary x axis?