You can day trade part-time, but it comes with its own set of challenges and considerations.
If you have a small window to trade in and it coincides with the opening of the the US market at 9:30 am ET that could be an ideal time as the volume is highest at the markets opening times and can afford very lucrative opportunities. It is conceivable to trade for an hour or two using this criteria.
If you cannot be available at 9:30 but want to trade the US session there is nothing to prevent you from dropping in at anytime. There is a slow down in the market from around Noon to 2 but volume picks back up in the late afternoon. So you could join the market at almost anytime for any length of time. The best advice would to be consistent at the time you trade especially when first starting out. This will give you the best chance of recognizing patterns and increase the impact of you market observation.
If you cannot trade the traditional RTH market and want to trade overnight, a good idea could be to trade one of the foreign markets at a time when one of the overnight sessions is opening. This is especially true of the Futures and Forex markets. Stock trading does not afford easy overnight and 24 hours day trading activity. There is limited pre-market and post-market activity.
The Globex market, is a 24 hour market offering Futures and commodities contracts to trade. Globex can be looked at the overnight market as compared to United States session. It can affords good opportunities at the open of the foreign market times when the opening volume tends to spike a bit higher.
For example if you were to trade the E-Mini S&P 500 futures in the overnight market of the European session your best trading would likely take place near the openings time of that market which is around 3am Eastern time.
The FOREX market is truly a global market as its products involve foreign assets. But there is higher activity at the start of sessions that can be taken advantage of.
Trading part time or during overnight can be challenging since volume is lighter than the US session but there are adjustment that can be made to trade at almost anytime the markets are open.