Got it.  Would appear as if the new flasher was DOA or I somehow blew it internally futzing with the leads.  Picked up another  2 prong one for $3  and tried it and it worked first time  I will chase a three wire version at a later time to see if I can get the indicator light lit. Thanks
Kim 

Hello and welcome!

As is customary when new people join I would like to suggest you fill in at least a little bit of your user profile so people know where you are located.  People on this board are generally quite happy to visit and assist when possible.

You are correct that your '63 would not have hazard flashers, only turn signals.  The original flasher would have been a 3-terminal device.  I no longer use the Lucas type flashers as the last one I bought was quite expensive and only lasted a very short while.  I use a generic "EL13" electronic flasher.  You could do the same since your car is negative ground.  If you prefer a less expensive and electromechanical flasher I believe that is a standard "550" flasher.  Both the 550 and EL13 flashers should be available at the local parts store.

Start your troubleshooting by inspecting the bulbs and make sure they are clean and not corroded.  Make sure all the bulbs are the Wattage identified in your manual.  Using the wrong Wattage bulb can prevent the flasher from operating properly.  You will find different Wattage bulbs are available at the parts store.  You don't need anything Mini specific.  Just match the appearance of the bulb and make sure it is the Wattage specified in the manual.

Make sure all the wire connections at the lamp housings are clean and without corrosion.

Make sure you have the wires on the correct flasher terminals.
The Lucas flasher will have its terminals marked: "B", "L", and "P".  
Aftermarket (U.S.) flashers will have their terminals marked: "X", "L", and "P".  
For both, "L" is for the "load" = lights, "P" = the dash indicator lamp.
"B" or "X" is the 12v supply.

If your car has the original cloth wrapped wiring harness it might be quite difficult to identify the wire colors.  Let us know if that is the case and let us know if you have and know how to use a multimeter.  It is a handy tool for electrical troubleshooting... particularly when you are trying to sort out faded wire colors.

Confirm that you have a green wire (with no other color stripe) on the flasher "B" (or "X") terminal.  Confirm that the flasher is getting power by turning the ignition key to the run position and measuring the voltage between the terminal of the green wire and the car's chassis.

Once you are sure that the green wire is in the correct location and has power, make sure the other two wire connections are on the correct terminals.  A light green with purple stripe wire should be on the "P" terminal.  A light green wire with brown stripe should be on the "L" terminal.  

Others will post shorter answers and suggestions soon.  Let us know what you find in the tests above.
 

Just got a MkI claiming to be a '63 Super Deluxe Morris Mini 850 from the UK and am sorting it out.  It is a bitsa driver (and I knew that going in and am good with that).  Has been converted to Neg grnd at some point.  Turn signals turn on (all are bright) with stalk but don't flash.  Assumed old flasher was bad (Wagner 223 2 prongs) Ordered a new  MKI flasher (3 prong GFU2103) in.  It does the same.  When I swap the wires at the flasher as suggested by instructions I get no turn lights at all.  Light on the stalk doesn't illuminate but that seems to be the 'third' wire on the flasher unit and I will chase that someday. There is a third wire but it doesn't seem to add value at this point (assume it is for dashboard warning light). I have swapped various combinations and there is only one the gets me the lights on (but not flashing).   Don't seem to have a switch for four way flashers and they aren't mentioned in the Drivers handbook so I assume those arrived later.  Any thoughts on how to troubleshoot and or where to stick a meter?  Sure it is something dumb but what? Thanks
Kim