What follows is not what overseas employment usually means. As a retiree you will not want to become bored and a little extra income is always useful. Importantly you do not wish to offend against your visa conditions. Local employment is often not permitted to retiree residents.
Perhaps a service club is the answer. In most countries there are organizations such as Rotary, Lions, Apex, Optimists, Soroptimists, JCI and many others. All of them do good work for the local community and fellowship at regular meetings is an attractive part of the activities. There has been a tendency for male predominance in these clubs but they are more open to active women members now either as part of the associations or as members of their own but separate body of the same group to which men belong. As a member of one of these clubs you will quickly build a circle of friends of retirees like yourself and of local citizens. Membership of a service club would not be considered as employment so you would be in no danger of offending restrictions that some countries place upon non-citizen residents. No work permit would be necessary for such "overseas employment".
It is possible that you have some specialized experience or skill. This could be employed in a voluntary manner. Perhaps you were involved in the Boy Scouts or Girl Guides in your previous country. There would probably be a welcome for you in the local bodies. If they do not exist then may be an approach to a local school would allow you to start such a group. A skill in needlework, knitting, carpentry or metal work would enable you to start a group in the local community to pass on these skills. Any artistic ability could be used in the same way. Again as a volunteer activity there would be no need for work permits. The same social benefits as accrue to members of service clubs would also be enjoyed by starting such groups.
There are no cash earnings with the volunteer works described above. It is very likely that a few meals and outings with the various clubs, groups and local members will be enjoyed. There is every opportunity to earn some pin money without being formally employed.
In many countries there are small cottage concerns too small to be called industries which produce local goods typical of the country or area. Purchasing such items to send overseas to friends or family for them to sell in a business might produce a good income. It could be of value to tourists who, by purchasing at your overseas store, avoid problems with customs and quarantine procedures. Such a venture would need extensive work in the set up phase and liaising with travel agents and other tourist organizations. Speculative purchasing and exports could be avoided if this was set up as an on-line business.
Organizing tour groups in cooperation with local businesses via the internet could also produce income without actual employment being involved. In both of these examples there are obvious benefits to local organizations of both small and medium sizes. Advertising overseas may be of interest to larger firms.
Selling goods produced overseas from catalogues, either in print form or on the internet to local people and businesses may also be outside of the "employment" definition. Orders and payment to the overseas suppliers would probably have to be in the name of the local buyer. Your experience in moving money internationally could well help your local customers. Your "commission" would come from the overseas exporters.
If you have internationally mobile skills opportunities for earning extra income are almost unlimited. Most countries do not tax citizens or residents on overseas earnings. The chances to continue as a computer programmer, web site builder or affiliate marketer are clear. Any expertise in writing such as copywriting, travel writing, ghost authorship, down to simple and small resume writing can all be done on line and payment received abroad. Tutoring in an appropriate area of your favoured abilities can also be done on-line or via e-mail. Care would have to be taken in the latter case with respect to taking on "local" students as this could be deemed as local employment.
Quite clearly there are many opportunities for "overseas employment" without offending local work permit regulations. The scale, which is always under your control, will determine how busy you become and how much tax free income you earn.
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