As an owner of a bespoke tweed suit, I decided to complete the look and buy a bowtie. Indy, in some scenes, is wearing a necktie, but in most scenarios, we can see him wearing a bowtie with suit. Unfortunately, most of the photos are somehow flimsy, but I am sure that he owns:
the red one

and
the brown one

I find the brown one more appealing, it greatly corresponds with the brown suit and beige shirt. But how to get a proper one? Magnoli had one for sale, but it is sold out now. So I decided to... order a bespoke bowtie!
I visited a small workshop, specialized in making ties, scarves and bowties, called tiestore.pl, in Warsaw, Poland. I showed them the photo above and asked what they have for. Here are the results:
Whole gallery:
https://imgur.com/a/baVeWTh" onclick="window.open(this.href);return false;
The last picture:

I finally choose a brown ancient madder silk you see in the last photo, and decided to order a classic, beautiful, diamond shaped bowtie (you can see the green one, made from grenadine - that's exactly the desired shape).
Ancient silk madder is a fabric that Indiana indeed could use for his ties. It has a subtle, chalky look, pairs great with tweeds and is a of the classic Ivy League style.
The bowtie will be ready in about 2-3 weeks. And of course, I am going to show it to you! Hope you enjoy my little review.