Plotting vectors on a datetime axis

I couldn’t figure out the type casting using numpy objects either, so I am not sure if it is possible using the methods in your post. But you can plot vectors with a datetime x-axis and Cartesian y-axis using a pandas.DataFrame as the data input:

import numpy as np
import pandas as pd
import datetime
import pygmt

x1 = np.array(["2010-06-01", "2011-06-01", "2012-06-01"], dtype="datetime64")
x2 = x = np.array(["2010-08-01", "2012-06-01", "2013-06-01"], dtype="datetime64")
y1=[3,2.5,3]
y2=[4,0.5,3]

data = pd.DataFrame(data={'x1': x1, 'y1': y1, 'x2': x2, 'y2': y2})
fig = pygmt.Figure()
fig.plot(
    data=data,
    region=[datetime.date(2010, 1, 1), datetime.date(2014, 1, 1), 0, 5],
    style="v0.25+e+s",
    frame=True
)
fig.show()