Hi,

This will be possible if you add the following to Appearance > Customize > Theme Options > Custom CSS:

.content .custom-title, .content .widget-title { text-shadow: 0 1px 2px #000; }

You can change the text shadow to your own needs. Maybe this will come in handy: https://css3gen.com/text-shadow/

Not specifically for the 2nd word in the widget title (if the title is longer than 2 words), but only for the rest of the title and the first word not or vice versa.

Combing the previous CSS and the remove the shadow for the first word:

.content .custom-title, .content .widget-title { text-shadow: 0 1px 2px #000; }
.content .custom-title span.light, .content .widget-title span.light { text-shadow: none; }

You're welcome