I am an electrician by trade & tech but long retired.
I did quite a lot of work for an appliance repair company - mainly vacuum cleaners & cleaning equipment.
Damaged mains cords was a really common problem & some of the items with retractable cords could take a fair bit of disassembling.
The old boss used to cut a short bit off the plug end first if the wiggle & flex test didn't help locate the problem.
I always had my trusted "Volt Stick" - test pencil that indicated mains voltage presence without actual contact.
That worked to show a break in the Active (Hot) conductor but the neutral conductor could be the fault.
I bought a double mains outlet with Double Pole switching that had connecting links between the two outlets & rewired the one side with reverse polarity - ie neutral to the active pin & active to the neutral pin.
I clearly marked the outlet with cross hatching & "Warning - Reverse Polarity" "Test Only."
I also got another single outlet which was left unwired.
The test outlet & unwired outlet were fixed to the test bench.
The first test was always a good inspection of the item, check the eaarthing if it is an earther housing, & then a physical test of pulling the cord through your fingers to detect any cuts or kinks etc in the flex to ensure that it is safe to handle the flex
Pulling the cord through your fingers is far better than just looking for faults.
By plugging into the normally wired outlet we could test for a broken Active Wire by running the test pencil along the cord.
By Plugging into the reverse polarity outlet the neutral was now live (hot) so the test pencil would locate a break in the Neutral Wire.
But sometimes the faults was at the recoil unit so a set of "Fool Killer" or "Suicide Leads" - mains cord with proper fully insulated crocodile clips could be fitting inside the unit & fitting the plug into the unwired socket to keep the protruding plug pins that now are live safe.
An alternative - perhaps better - would be to buy one of the LOTO - Lock Out Tag Out hard plastic plug covers that use a padlock to lock a damaged item plug so that equipment can't be used until repaired.
Then the "Fool Killer" leads could be used to repeat the two tests with power from the opposite end of the lead.
This would locate the fault most of the time.
At home I have a foot switch for use at any time that I may wish to disconnect power quickly (such as when I use a Fool Killer lead) & I use RCD / Safety Switch / Earth Leakage protection on all my circuits.
I have 30mA protection on the house but a 10mA Outlet on the bench.
My shed bench also has a trip cord switch used on conveyor belts with the cord along the front of the bench so that pushing on it cuts all power.
I got a few of those switches cheap on eBay once & since I normally work alone I decided it couldn't hurt to use one.
I also normally have a lead with stripped ends with some WAGO 222 connectors on it.
The WAGO 222 connectors are used for permanent wiring connections & I believe they are even rated for mines use.
They have a lever action which makes it really quick & easy to use when you wish to test something with wire ends.
One big advantage is the connector will safely & firmly hold a wide range of wire sizes.
The same connector can be used to hold a 2.5mm CSA (Cross Section Area) wire in one tunnel & a single strand from a 7 strand 1.5mm CSA will be kept so firmly in the next tunnel that the strand will break before it will slip.
The WAGO connectors are so quick & easy to use that you will use them first & avoid the tendency to be lazy & use a Fool Killer lead to test something withe wire ends on it.