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However, the way they're wired, I believe if the hazard flasher goes on the blink, so does the turn signal flasher.
I replaced the flasher unit with one from the local parts store.
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a) You are almost correct. See
https://www.mgexperience.net/phorum/read.php?1,465525 for more details on this. (for some reason, the comma in this URL cuts off the last part of the link, so you'll have to cut and paste it into your browser to make it work). The hazard flasher failing won't stop the turn signals from working, but a failure of the hazard switch might.
b) This will work, but you need to be aware that these are not turn signal flashers, but hazard flashers. They'll work, but you won't get a warning if one of the turn signal bulbs is out. With the OEM turn signal flasher, if one bulb is out (or the wiring/grond connection is bad), the flash rate slowed to a crawl or stopped altogether to let you know about it. These flashers will continue to flash at the same rate even with one bulb out, so you will have to get into the habit of checking your turn signal bulbs occasionally.