My car is a Toyota Town Ace, year 1993.
63W means about 80W into the inverter so the battery will only last several hours (by comparison, low beam is ~110W plus ~30-50W in other bulbs).
80W into the inverter means about 6-8A which ca be too much for some cig sockets. You should use a direct battery connection (via fuse).
If the fridge is a compressor type, then it may have a big inrush/start-up current that may not suit the inverter.
By comparison, I have a 40L fridge/freezer that takes a peak of 2.5A at 12V (~30W) but generally under 1.5A and only when it is chilling. I reckon that will last about 24 hours on my car battery (40AH).
For what it's worth....
I laughed at "idiots" that spent >$1000 on coolers etc when I bought my $145 40L Peltier.
I am now one of those idiots.
Why?
The Peltier consumed 5A-8A (most of the time) and only cooled to 20C below ambient.
I needed another $1,000 of solar panels to meets its power needs (plus battery(s), and then still relying on the chance of sun etc for a measly "20C below").
So a new $1,400 40L fridge was worthwhile based on cost alone.
I got a preloved Engel MT45 Mk2 for $900 of eBay. (I had resigned myself to buying new - the saving for 2nd hand was not great, and I was determined to get the newer 2.5A max models; 5A could mean double the panels and batteries etc.)
A max of 2.5A though I have only seen 1.25A for fridge use in 30C ambient days. But it will cool to -19C in ~40-45C ambient. (I intended to get a 45L "3-day Esky" and use the Engel to freeze ice for it etc.)
The earlier models were a peak of 5A with a normal of 2.5A.
But compressor fridges are on less than Peltier due to better insulation and better efficiency (quicker cooling).
On paper I was torn between Engel and Waeco, but after seeing them in person, I wrote off Waeco. (Flimsy & bad fitting lids etc.)
Also an experienced source claimed a 10:1 repair rate of Waeco to Engel.
In fact I rarely see Waecos when I'm camping, but that may be because I only took notice of the Engels
(I'd seek views).
I originally expected to use a 3-way until I found they could not be used when mobile, and they are very electricity hungry. (I wonder why there are no solar-heated absorbtion types? Maybe one day I'll look into that.)
FYI trivia:
The Engel 10A "thermal fuse" in the cig plug is only thermal to protect the user's vehicle etc from bad cig-sockets - ie, prevent fire. The thermal is NOT required for the fridge itself. (So many forums fail to recognise that!)
So if you are happy that your cig socket won't flame, then ordinary fuses are fine.
And if it's a max of 2.5A, why not use a 5A instead? (Then again, if cable etc is rated for 10A, why bother with 5A?)
But the fridge has its own fuse (blade).
I replaced the Engel's 10A blade fuse with a self-resetting circuit breaker. (Actually I use a 5A since the max should only be 2.5A, but I carry spares...)
PS - My Peltier is great when running with the car. (That was what started me down the dual-battery and UIBI road.)
And even when not used
electrically, it is better than a plain Esky - ice lasts typically twice as long due to better insulation.
But those newer "super-eskies" are far superior - eg:
techniice iceboxes