Let's look at the East Asian admixture among South Asians and other surrounding populations from a previous admixture run (K=12).

I have listed the different kinds of East Asian admixture components among selected populations. The three relevant components are:

1. Southeast Asian: Highest among the Dai, Cambodians, Lahu and Malay, this is the most common East Asian component among South Asians.
2. Northeast Asian: Highest among the Naga, Nysha, Japanese and north Han.
3. Siberians: Highest among the Nganassans and Evenkis, this is lowest among South Asians overall. While this is not quite Turkic, it is the one most related to them.

Let's look at the total East Asian percentage among South Asians.

As expected, the eastern part of South Asia is where we see most of the East Asian admixture.

Now instead of looking at the absolute percentages of Southeast Asian admixture, let's look at the Southeast Asian component as a percentage of total East Asian component.

South and East India seem like mostly Southeast Asian admixture.

Now the same map for Northeast Asian as a proportion of total East Asian:

The Northeast Asian component dominates along the northern border of South Asia.

Finally the Siberian:

Compared to the other two, Siberian component is fairly low among South Asians, so it's difficult to separate the noise from real admixture here. Most of the peaks you see are among populations that have low East Asian admixture.