The *only* 'work at home' deal I heard about was when some one started a small manufacturing biz in his garage - getting a small contract to build relatively simple circuits.
You may not consider that 'engineering' - but was in fact manufacturing engineering building electronic circuit boards. He went on to build a multi-million dollar enterprise in relatively short period of time.
But to do traditional 'electronic engineering' I would think those lucky enough to do that at home have either already built a level of trust with their employer (read: lots of experience) - or has a handful of clients who dont mind meeting at someones home or coffee shops to talk business.
Keep in mind - most engineers work in a team. Working with techs to build their designs, develop ways to manufacture, lower costs, work with QC persons to verify operating condtions wont be a problem.. etc. etc.
So Id say, these jobs are short in supply, and *who* wouldn't like to work at home.?? (in other word, the limited opportunities are in high demand by a relatively large group of people, given the fuel costs these days)