What are the best times in early April to contact Japan on 40M and 20M from Pennsylvania?
Around sunrise and sunset (both yours and theirs), to take advantage of "grayline" propagation, which has lower loss than daytime propagation, at higher frequencies than nighttime propagation. In April, Japanese sunset comes a few hours before your sunrise, around 5am. 40 meters may open around that time, and 20 meters may open right around your sunrise. At around 7pm, the sun will be rising in Japan, and there is a good chance of another 20m opening until your sunset.
Surprisingly, you might find better luck between October and February. Although northern-hemisphere propagation is overall less during those months, the shorter length of day means that your sunset and Japan's sunrise align more favorably, and your entire path will be "in grayline". There is also a brief period in June where your sunrise and Japan's sunset align well.
A nice tool to get an idea for these questions is VOACAP. If you go to their newly redesigned HF planner, you can drag the red marker to your location, and the blue marker to where you want to talk to (or select "W Harrisburg PA" and "JA Tokyo" in the TX and RX QTH dropdowns). You may also adjust the mode, power, and antenna dropdowns. Then scroll to the bottom and click "All Year" for a month-by-month chart of bands and times, and you will see what I mean.
This is a great use case for VOACAP. You tell it where the stations are:
And then you can click the "Prop Wheel" button to see what times on what bands are good:
Here we can see from 20:00 to 03:00 UTC are OK on 20 meters, and 40 meters is good from 08:00 to 11:00 UTC.
VOACAP takes into account your power, mode, antennas, time of day, and time of year, all of which can significantly alter your chances of making a contact. For this run I used CW at 100 watts, and the default antennas which include a dipole 33 feet off the ground on 40m, and a 3 element Yagi at the same height for 20 meters, on April 13, 2020.