Type of capacitor to bridge X10 signals in household power
I like X-10, use it myself, and have put it into several friends' homes.  What has worked for me for decades is a 0.22 uF plastic box capacitor, rated X, X1, or X2.  This is a film capacitor similar to the one pictured, but rated for continuous connection across AC lines such as Line-to-Line (240 Vac).  Most are rated for something like 275 Vac.

This type of capacitor is called "self-healing".  If an internal short happens, the transient current blows away the shorting material, often such that the part continues to have enough capacitance to function normally.

https://www.ecicaps.com/tech-tools/technical-papers/self-healing-affect-metallized-capacitors/



UPDATE:  Seeing the added photos of the old cap with the "104" marking (0.1 uF) jogged a memory.  Long ago I knew that was the recommended value, and used it for a while.  But as I expanded the X-10 stuff around the house, some controllers could not "reach" some devices, so I increased the value to 0.22 uF and that solved it.  That is why I recommend 0.22 uF over 0.1 uF.  If you want to compromise, 0.15 uF also will work.