How to setup ip addressing on 2nd pi network interface

Question

I have rasp pi 3 and I purchased this usb ethernet adapter:

https://www.amazon.co.uk/gp/product/B00M77HLII/ref=ppx_yo_dt_b_asin_title_o03_s00?ie=UTF8&psc=1

The device was detected by the pi without me doing anything and comes up as eth1. Initially it was using a dynamic ip address from my dhcp server, but I changed the config of /etc/dhcpcd.conf as follows:

# Example static IP configuration:
interface eth1
static ip_address=192.168.4.10/24
static ip6_address=fd51:42f8:caae:d92e::ff/64
static routers=192.168.4.1
#static domain_name_servers=192.168.0.1 8.8.8.8 fd51:42f8:caae:d92e::1

I have an ethernet cross-over cable from the eth1 port to an old laptop running windows 7 configured with:

IP: 192.168.4.1 subnet mask: 255.255.255.0

From the Windows laptop I can ping 192.168.4.10 (IP of pi eth1) and get a success response. But when I ping from the pi to 192.168.4.1 it doesn't work:

i@raspberrypi:~ $ ping 192.168.4.1
PING 192.168.4.1 (192.168.4.1) 56(84) bytes of data.
^C
--- 192.168.4.1 ping statistics ---
9 packets transmitted, 0 received, 100% packet loss, time 8328ms

Am I missing some config on the pi? How can I fix this.

I want to be able to ping the Windows laptop from the pi.

Current pi networking:

pi@raspberrypi:~ $ ifconfig
eth0: flags=4163<UP,BROADCAST,RUNNING,MULTICAST>  mtu 1500
    inet 192.168.0.78  netmask 255.255.255.0  broadcast 192.168.0.255
    inet6 fe80::707f:94c4:2008:ef22  prefixlen 64  scopeid 0x20<link>
    ether b8:27:eb:a7:1a:5e  txqueuelen 1000  (Ethernet)
    RX packets 544  bytes 46335 (45.2 KiB)
    RX errors 0  dropped 0  overruns 0  frame 0
    TX packets 267  bytes 33558 (32.7 KiB)
    TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0

eth1: flags=4163<UP,BROADCAST,RUNNING,MULTICAST>  mtu 1500
    inet 192.168.4.10  netmask 255.255.255.0  broadcast 192.168.4.255
    inet6 fe80::7add:e44a:bb51:a65e  prefixlen 64  scopeid 0x20<link>
    inet6 fd51:42f8:caae:d92e::ff  prefixlen 64  scopeid 0x0<global>
    ether a0:ce:c8:79:e5:89  txqueuelen 1000  (Ethernet)
    RX packets 389  bytes 82178 (80.2 KiB)
    RX errors 0  dropped 0  overruns 0  frame 0
    TX packets 122  bytes 13074 (12.7 KiB)
    TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0

lo: flags=73<UP,LOOPBACK,RUNNING>  mtu 65536
    inet 127.0.0.1  netmask 255.0.0.0
    inet6 ::1  prefixlen 128  scopeid 0x10<host>
    loop  txqueuelen 1000  (Local Loopback)
    RX packets 30  bytes 3023 (2.9 KiB)
    RX errors 0  dropped 0  overruns 0  frame 0
    TX packets 30  bytes 3023 (2.9 KiB)
    TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0